UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13G
                    Under the Securities Exchange Act of 1934

                              (Amendment No. 1)(2)


            AboveNet, Inc. (formerly Metromedia Fiber Network, Inc.)
                     --------------------------------------
                                (Name Of Issuer)

                     Common Stock, par value $0.01 per share
                     --------------------------------------
                         (Title of Class of Securities)

                                    00374N107
                     ---------------------------------------
                                 (CUSIP Number)

                                January 29, 2004
                     ---------------------------------------
             (Date of Event Which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

         [ ]  Rule 13d-1(b)
         [X]  Rule 13d-1(c)
         [ ]  Rule 13d-1(d)

1 The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("the Act") or otherwise subject to the liabilities of that section of the
Act but shall be subject to all other provisions of the Act (however, see the
Notes).

2 The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("the Act") or otherwise subject to the liabilities of that section of the
Act but shall be subject to all other provisions of the Act (however, see the
Notes).





CUSIP NO. 00374N107                     13G

1        NAME OF REPORTING PERSON
         SS. OR IRS IDENTIFICATION NO. OF ABOVE PERSON

                             Verizon Communications Inc. #23-2259884

2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                    (A) [ ]
                                                                    (B) [X]

3        SEC USE ONLY

4        CITIZENSHIP OR PLACE OF ORGANIZATION

         Delaware

                           5      SOLE VOTING POWER
        NUMBER OF                 0 (See Item 4)
         SHARES
 BENEFICIALLY OWNED BY     6      SHARED VOTING POWER
         EACH                     8,664 (See Item 4)
       REPORTING
        PERSON             7      SOLE DISPOSITIVE POWER
         WITH                     0 (See Item 4)

                           8      SHARED DISPOSITIVE POWER
                                  8,664 (See Item 4)

9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         8,664 (See Item 4)

10       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
         See Item 4                                                    [X]

11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9
         Less than 1% (See Item 4)

12       TYPE OF REPORTING PERSON*
         HC


                                       2


CUSIP NO. 00374N107                   13G

1        NAME OF REPORTING PERSON
         SS. OR IRS IDENTIFICATION NO. OF ABOVE PERSON
         Verizon Investments Inc. #13-3191789

2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                       (A)[ ]
                                                                       (B)[X]

3        SEC USE ONLY

4        CITIZENSHIP OR PLACE OF ORGANIZATION
         Delaware

                           5      SOLE VOTING POWER
        NUMBER OF                 0 (See Item 4)
         SHARES
   BENEFICIALLY OWNED BY   6      SHARED VOTING POWER
          EACH                    8,664 (See Item 4)
       REPORTING
         PERSON            7      SOLE DISPOSITIVE POWER
          WITH                    0 (See Item 4)

                           8      SHARED DISPOSITIVE POWER
                                  8,664 (See Item 4)

9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         8,664 (See Item 4)

10       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
         See Item 4

11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9
         Less than 1% (See Item 4)

12       TYPE OF REPORTING PERSON*
         HC




CUSIP NO. 00374N107                               13G

1        NAME OF REPORTING PERSON
         SS. OR IRS IDENTIFICATION NO. OF ABOVE PERSON
         Verizon Global Networks Inc. #54-1885546

2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                    (A)[ ]
                                                                    (B)[X]

3        SEC USE ONLY

4        CITIZENSHIP OR PLACE OF ORGANIZATION
         Delaware

                           5      SOLE VOTING POWER
        NUMBER OF                 0 (See Item 4)
         SHARES
  BENEFICIALLY OWNED BY    6      SHARED VOTING POWER
          EACH                    0 (See Item 4)
        REPORTING
          PERSON           7      SOLE DISPOSITIVE POWER
           WITH                   0 (See Item 4)

                           8      SHARED DISPOSITIVE POWER
                                  0 (See Item 4)

9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         0 (See Item 4)

10       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
         See Item 4

11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9
         0% (See Item 4)

12       TYPE OF REPORTING PERSON*
         HC


                                       4




Item 1.

         (a)  Name of Issuer

                  AboveNet, Inc. (formerly Metromedia Fiber Network, Inc,)

         (b)  Address of Issuer's Principal Executive Offices

                  360 Hamilton Avenue
                  White Plains, New York  10601

Item 2.

         (a)  Name of Persons Filing

                  Verizon Communications Inc. ("Verizon")
                  Verizon Investments Inc. ("VII")
                  Verizon Global Networks Inc. ("VGNI")
                  Verizon, VII and VGNI collectively may be referred to herein
                  as the "Reporting Persons".

         (b)  Address of Principal Business Office or, if none, Residence

                  Verizon
                  1095 Avenue of the Americas
                  New York, New York 10036

                  VII
                  3900 Washington Street
                  Wilmington, Delaware 19802

                  VGNI
                  1320 N. Court House Road
                  Arlington, Virginia 22201



         (c)  Citizenship

                  Each of Verizon, VII and VGNI is incorporated under the laws
                  of the State of Delaware.

                                       5



         (d)  Title of Class of Securities

                  Common Stock, par value $0.01 per share

         (e)  CUSIP Number

                  00374N107

Item 3. If this statement is filed pursuant to Rule 13d-1(b), or 13d-2(b), check
whether the person filing is a:


(a)   [ ] Broker or Dealer registered under Section 15 of the Exchange Act

(b)   [ ] Bank as defined in Section 3(a)(6) of the Exchange Act

(c)   [ ] Insurance Company as defined in Section 3(a)(19) of the Exchange Act

(d)   [ ] Investment Company registered under Section 8 of the Investment
          Company Act

(e)   [ ] Investment Adviser in accordance with Rule 13d-1(b)(1)(ii)(E)

(f)   [ ] Employee Benefit Plan or Endowment Fund in accordance with
          13d-1(b)(1)(ii)(F)

(g)   [ ] Parent Holding Company or Control Person in accordance with Rule
          13d-1(b)(1)(ii)(G)

(h)   [ ] Savings Association as defined in Section 3(b) of the Federal Deposit
          Insurance Act

(i)   [ ] Church Plan that is excluded from the definition of an investment
          company under Section 3(c)(14) of the Investment Company Act

(j)   [ ] Group, in accordance with Rule 13d-1(b)(1)(ii)(J)


Item 4.  Ownership

         (a)  Amount Beneficially Owned:

         The Issuer filed a Current Report on Form 8-K with the Securities and
         Exchange Commission ("SEC") on September 8, 2003 in which it reported
         that it had emerged from Chapter 11 of the U.S. Bankruptcy Code on
         September 8, 2003 (the "Effective Date"), pursuant to the Issuer's
         Second Amended Plan of Reorganization (the "Plan"). In connection
         therewith, the Reporting Persons acquired beneficial ownership of
         shares of the Common Stock of the Issuer as of the Effective Date
         pursuant to the Plan, as well as warrants and other rights to purchase
         shares of Common Stock of the Issuer in exchange for claims of the
         Reporting Persons against the Issuer and its subsidiaries. As a result
         of several separate transactions, the last of which settled on January
         29, 2004, VGNI no longer beneficially owns any shares of Common Stock
         of the Issuer and VII is no longer the record holder of any shares of
         Common Stock of the Issuer. VII holds warrants to purchase 8,664 shares
         of Common Stock of the Issuer and may be deemed to be the beneficial
         owner of the 8,664 shares which are issuable upon exercise of those
         warrants.

                                       6



         VII is a direct wholly owned subsidiary of Verizon and by virtue of
         their relationships, Verizon and VII may be deemed to have shared power
         to vote and dispose of, or to direct the vote and disposition of, the
         shares that may be deemed to be beneficially owned by VII through the
         right to exercise the warrants held by VII.

         As of the date hereof, the Reporting Persons have been only able to
         estimate the number of shares of Common Stock they may be deemed to
         beneficially own because the Reporting Persons have not yet received
         information sufficient to determine with precision the number of shares
         of Common Stock receivable in the future pursuant to the Plan. Such
         number of shares cannot be finally determined until the actual amount
         of Allowed Claims (as defined in the Plan) has been finally determined
         by the Issuer. The Reporting Persons believe that some number of
         additional shares of Common Stock of the Issuer may be receivable by
         them in the future pursuant to the Plan but they have no present
         knowledge that any such distribution of shares is likely to occur
         within the next 60 days. In addition, the Reporting Persons have reason
         to believe that no such distribution would result in any of them being
         deemed to be the beneficial owner of more than 5% of the shares of
         Common Stock of the Issuer.

(b)      Percent of Class:

         The responses of the Reporting Persons to Row (11) of the cover pages
         of this Schedule 13G are incorporated herein by reference. For purposes
         of calculating the percent of Common Stock that may be deemed to be
         beneficially owned, the Reporting Persons estimate that there were
         approximately 7,509,660 shares of Common Stock of the Issuer
         outstanding as of the close of business on February 5, 2004, based on
         information received from the transfer agent for the Issuer's Common
         Stock. For purposes of such calculation for Verizon and VII, an
         additional 8,664 shares of Common Stock that VII has the right to
         acquire pursuant to warrants that may be deemed to be beneficially
         owned by it, are to be deemed outstanding, in accordance with Rule
         13d-3 under the Exchange Act.

         As of the date hereof, the Reporting Persons have been only able to
         estimate their percent of class that may be deemed to be beneficially
         owned because the Reporting Persons have not yet received information
         sufficient to determine with precision (i) the number of shares of
         Common Stock received or receivable pursuant to the Plan and (ii) the
         number of shares of Common Stock outstanding. Such numbers of shares
         cannot be finally determined until the actual amount of Allowed Claims
         (as defined in the Plan) has been finally determined by the Issuer.



                                       7



(c)      Number of shares as to which such person has:

                    (i) sole power to vote or to direct the vote, (ii) shared
                    power to vote or to direct the vote, (iii) sole power to
                    dispose or to direct the disposition, and (iv) shared power
                    to dispose or to direct the disposition, in each case are
                    incorporated by reference from the responses of the
                    Reporting Persons to Rows (5) through (8) of the cover pages
                    of this Schedule 13G and Item 4(a) hereof.

Item 5.  Ownership of Five Percent or Less of a Class:

         This statement is being filed to report the fact that as of the date
hereof the Reporting Persons have ceased to be the beneficial owners of more
than five percent of the Common Stock of the Issuer.

Item 6.  Ownership of More Than Five Percent on Behalf of Another Person:

         Not Applicable.

Item 7. Identification and Classification of the Subsidiary Which Acquired the
Security Being Reported On by the Parent Holding Company:

         See Item 4.

Item 8.  Identification and Classification of Members of the Group:

         Not Applicable.

Item 9.  Notice of Dissolution of Group:

         Not Applicable.

Item 10.  Certifications:

(b) By signing below I certify that, to the best of my knowledge and belief, the
securities referred to above were not acquired and are not held for the purpose
of or with the effect of changing or influencing the control of the issuer of
the securities and were not acquired and are not held in connection with or as a
participant in any transaction having that purpose or effect.




                                       8





                                   SIGNATURES

         After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

                                   February 10, 2004
                                   ---------------------------------------

                                   VERIZON COMMUNICATIONS INC.

                                   /s/Marianne Drost
                                   ---------------------------------------
                                   Signature

                                   Marianne Drost -
                                   Senior Vice President, Deputy General
                                   Counsel and Corporate Secretary
                                   ---------------------------------------
                                   Name/Title

                                   VERIZON INVESTMENTS INC.

                                   /s/Janet M. Garrity
                                   ---------------------------------------
                                   Signature

                                   Janet M. Garrity - President and Treasurer
                                   ---------------------------------------
                                            Name/Title

                                   VERIZON GLOBAL NETWORKS INC.

                                   /s/Robert S. Fitzmire
                                   ---------------------------------------
                                   Signature


                                   Robert S. Fitzmire - Treasurer
                                   ---------------------------------------
                                   Name/Title



                                       9




                                                                       EXHIBIT A

                         AGREEMENT AS TO JOINT FILING OF
                                  SCHEDULE 13G

         The undersigned hereby agree and consent to the joint filing on their
behalf of this Schedule 13G.

                                    September 17, 2003
                                    --------------------------------------

                                    VERIZON COMMUNICATIONS INC.

                                    /s/Marianne Drost
                                    --------------------------------------
                                    Signature

                                    Marianne Drost -
                                    Senior Vice President, Deputy General
                                    Counsel and Corporate Secretary
                                    --------------------------------------
                                    Name/Title

                                    VERIZON INVESTMENTS INC.

                                    /s/Janet M. Garrity
                                    --------------------------------------
                                    Signature

                                    Janet M. Garrity - President and Treasurer
                                    --------------------------------------
                                    Name/Title

                                    VERIZON GLOBAL NETWORKS INC.

                                    /s/Robert S. Fitzmire
                                    --------------------------------------
                                    Signature

                                    Robert S. Fitzmire - Treasurer
                                    --------------------------------------
                                    Name/Title

                                       10