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

                                  SCHEDULE 13G
                                (RULE 13d - 102)

             Information to be included in statements filed pursuant
           to Rules 13d-1(b), (c) and (d) and amendments thereto filed
                              pursuant to 13d-2(b)

                               (AMENDMENT NO. 1)*

                            Harken Energy Corporation
                                (Name of Issuer)

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

                                    412552309
                                 (CUSIP Number)


                                December 31, 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)


 *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
                  disclosures provided in a prior cover page.

    The information required on 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 ("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).

                       (Continued on the Following Pages)

                                  (Page 1 of 4)


CUSIP No. 412552309                   13G                     Page 2 of 4 Pages


1.      NAMES OF REPORTING PERSONS
        I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)

               The Tail Wind Fund Ltd.

2.      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

        (a) [ ]
        (b) [ ]

3.      SEC USE ONLY

4.      CITIZENSHIP OR PLACE OF ORGANIZATION

                A British Virgin Islands corporation

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH:

5.      SOLE VOTING POWER

                18,977,459

6.      SHARED VOTING POWER

                     0

7.      SOLE DISPOSITIVE POWER

                18,977,459

8.      SHARED DISPOSITIVE POWER

                     0

9.      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

               18,977,459

10.     CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9)
        EXCLUDES CERTAIN SHARES*       [ ]

11.     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                     8.25%

12.     TYPE OF REPORTING PERSON*

                     CO

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!

CUSIP No. 412552309                   13G                     Page 3 of 4 Pages

This statement is filed pursuant to Rule 13d-2(b) with respect to the common
stock (the "Common Stock") of Harken Energy Corporation beneficially owned by
the Reporting Person specified herein as of December 31, 2004 and amends and
supplements the Schedule 13G dated October 12, 2004 and filed by the Reporting
Person on October 20, 2004 (the "Schedule 13G"). Except as set forth herein, the
Schedule 13G is unmodified.

ITEM 4.   OWNERSHIP.

     Provide the following information regarding the aggregate number and
percentage of the class of securities of the issuer identified in Item 1.

     (a)  Amount beneficially owned:

               18,977,459 shares of Common Stock

               Tail Wind beneficially owns a total of 18,977,459 shares of
          Common Stock, including (i) 2,220,623 shares of Common Stock held by
          Tail Wind, (ii) 1,672,727 shares of Common Stock into which 9,200
          shares of Series L Convertible Preferred Stock are convertible,
          assuming a conversion price of $0.55 and no accrued dividends, which
          were issued to Tail Wind on May 28, 2004, (iii) 7,666,667 shares of
          Common Stock into which 46,000 shares of Series M Convertible
          Preferred Stock are convertible, assuming a conversion price of $.60
          and no accrued dividends, which were issued to Tail Wind on or about
          October 12, 2004, (iv) 3,382,353 shares of Common Stock into which
          warrants are exercisable which were issued to Tail Wind on May 28,
          2004, and (v) 4,035,088 shares of Common Stock into which warrants are
          exercisable which were issued to Tail Wind on or about October 12,
          2004.

     (b)  Percent of class:
 
               Tail Wind's aggregate beneficial ownership of 18,977,459 shares
          of Common Stock as of December 31, 2004 constitutes 8.25% of all of
          the outstanding shares of Common Stock, based upon 207,809,100 shares
          of Common Stock outstanding as of November 1, 2004 plus the 5,436,342
          shares of Common Stock issued to Tail Wind and Solomon Strategic
          Holdings, Inc. since such date.

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

          (i)   Sole power to vote or to direct the vote

                    18,977,459

          (ii)  Shared power to vote or to direct the vote

                    Not applicable.

          (iii)  Sole power to dispose or to direct the disposition of

                    18,977,459

          (iv)  Shared power to dispose or to direct the disposition of

                    Not applicable.

ITEM 10.  CERTIFICATION.

By signing below the undersigned certifies that, to the best of its 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.


CUSIP No. 412552309                   13G                     Page 4 of 4 Pages

                                    SIGNATURE

     After reasonable  inquiry and to the best of its knowledge and belief,  the
undersigned  certifies that the information set forth in this statement is true,
complete, and correct.


Dated: January 13, 2005                       THE TAIL WIND FUND LTD.


                                              By: /s/ Andrew P. MacKellar
                                                  -----------------------------
                                                  Andrew P. MacKellar, Director