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

                                  SCHEDULE 13G

                    Under the Securities Exchange Act of 1934

                               (Amendment No. 2)*

                            FALCONSTOR SOFTWARE, INC.
                                (Name of Issuer)

                         Common Stock, $0.001 par value
                         (Title of Class of Securities)

                                    306137100
                                 (CUSIP Number)

                                December 31, 2003
              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 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 ("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).


                                  Page 1 of 8


CUSIP NO. 306137100                   13G

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

     Eli Oxenhorn
--------------------------------------------------------------------------------
2.   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

                                                                 (a)  |_|
                                                                 (b)  |_|
--------------------------------------------------------------------------------
3.   SEC USE ONLY


--------------------------------------------------------------------------------
4.   CITIZENSHIP OR PLACE OF ORGANIZATION

     United States
--------------------------------------------------------------------------------
  NUMBER OF    5.   SOLE VOTING POWER

   SHARES           2,898,932 shares                                        6.3%
               -----------------------------------------------------------------
BENEFICIALLY   6.   SHARED VOTING POWER

  OWNED BY          306,077 shares                                          0.7%
               -----------------------------------------------------------------
    EACH       7.   SOLE DISPOSITIVE POWER

  REPORTING         2,898,932 shares                                        6.3%
               -----------------------------------------------------------------
   PERSON      8.   SHARED DISPOSITIVE POWER

    WITH            306,077 shares                                          0.7%
--------------------------------------------------------------------------------
9.   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     3,205,009 shares
--------------------------------------------------------------------------------
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
     (SEE INSTRUCTIONS)

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

     6.9%
--------------------------------------------------------------------------------
12.  TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

     IN
--------------------------------------------------------------------------------


                                  Page 2 of 8


CUSIP NO. 306137100                   13G

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

     Eli Oxenhorn Family Limited Partnership
--------------------------------------------------------------------------------
2.   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

                                                                 (a)  |_|
                                                                 (b)  |_|
--------------------------------------------------------------------------------
3.   SEC USE ONLY


--------------------------------------------------------------------------------
4.   CITIZENSHIP OR PLACE OF ORGANIZATION

     New York
--------------------------------------------------------------------------------
  NUMBER OF    5.   SOLE VOTING POWER

   SHARES           306,077 shares                                          0.7%
               -----------------------------------------------------------------
BENEFICIALLY   6.   SHARED VOTING POWER

  OWNED BY          0 shares                                                0%
               -----------------------------------------------------------------
    EACH       7.   SOLE DISPOSITIVE POWER

  REPORTING         306,077 shares                                          0.7%
               -----------------------------------------------------------------
   PERSON      8.   SHARED DISPOSITIVE POWER

    WITH            0 shares                                                0%
--------------------------------------------------------------------------------
9.   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     306,077 shares
--------------------------------------------------------------------------------
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
     (SEE INSTRUCTIONS)

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

     0.7%
--------------------------------------------------------------------------------
12.  TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

     PN
--------------------------------------------------------------------------------


                                  Page 3 of 8


CUSIP NO. 306137100                   13G

      This statement constitutes Amendment No. 2 to the Schedule 13G previously
filed by the Reporting Persons. No changes in any information previously
reported have occurred, except as set forth in this or prior Amendments.

Item 1.

            (a)   FalconStor Software, Inc.

            (b)   Address of Issuer's Principal Executive Offices

                  3 Huntington Quadrangle
                  Melville, New York 11747

                  Common Stock, $0.001 per share (CUSIP No.306137100)

Item 2.

1.          (a)   Name of Person Filing:

                  Eli Oxenhorn

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

                  56 The Intervale
                  Roslyn Heights, New York 11576

            (c)   Citizenship:

                  United States

            (d)   Title of Class of Securities:

                  Common Stock, $0.001 par value per share

            (e)   CUSIP Number:

                  306137100

2.          (a)   Name of Person Filing:

                  Eli Oxenhorn Family Limited Partnership

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

                  56 The Intervale
                  Roslyn Heights, New York 11576

            (c)   Place of Organization:

                  New York

            (d)   Title of Class of Securities:

                  Common Stock, $0.001 par value per share

            (e)   CUSIP Number:

                  306137100

Item 3. If this statement is filed pursuant to ss.240.13d-1(b) or 240.13d-2(b)
        or (c), check whether the person is a:

      (a)   |_|   Broker or dealer registered under section 15 of the Act (15
                  U.S.C.78o)

      (b)   |_|   Bank as defined in section 3(a)(6) of the Act (15 U.S.C. 78c).


                                  Page 4 of 8


CUSIP NO. 306137100                   13G

      (c)   |_|   Insurance company as defined in section 3(a)(19) of the Act
                  (15 U.S.C. 78c).

      (d)   |_|   Investment company registered under section 8 of the
                  Investment Company Act of 1940 (15 U.S.C. 80a-8).

      (e)   |_|   An investment adviser in accordance with
                  ss.240.13d-1(b)(1)(ii)(E);

      (f)   |_|   An employee benefit plan or endowment fund in accordance with
                  ss.240.13d-1(b)(1)(ii)(F);

      (g)   |_|   A parent holding company or control person in accordance with
                  ss.240.13d-1(b)(1)(ii)(G);

      (h)   |_|   A savings associations as defined in Section 3(b) of the
                  Federal Deposit Insurance Act (12 U.S.C. 1813);

      (i)   |_|   A church plan that is excluded from the definition of an
                  investment company under section 3(c)(14) of the Investment
                  Company Act of 1940 (15 U.S.C. 80a-3);

      (j)   |_|   Group, in accordance with ss.240.13d-1(b)(1)(ii)(J).

Item 4. Ownership

      1.    Eli Oxenhorn:

            (a)   Amount Beneficially Owned: 3,205,009(1),(2),(3) shares

            (b)   Percent of Class: 6.9%

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

                  (i)   sole power to vote or to direct the vote: 2,898,932(1)
                        shares

                  (ii)  shared power to vote or to direct the vote:
                        306,077(2),(3) shares

                  (iii) sole power to dispose or to direct the disposition of:
                        2,898,932(1) shares

                  (iv)  shared power to dispose or to direct the disposition of:
                        306,077(2),(3) shares

----------

(1)   Consists of 2,887,932 shares of Common Stock held by Mr. Oxenhorn, 3,500
      shares held by the Eli Oxenhorn SEP IRA account and 8,000 shares held by
      the Eli Oxenhorn Rollover IRA Account.

(2)   Consists of 306,077 shares of Common Stock held by the Eli Oxenhorn Family
      Limited Partnership.

(3)   The reporting person disclaims beneficial ownership of these securities,
      except to the extent of his equity interest therein.


                                  Page 5 of 8


CUSIP NO. 306137100                   13G

      2.    Eli Oxenhorn Family Limited Partnership:

            (a)   Amount Beneficially Owned: 306,077(2) shares. Reporting person
                  is the general partner of the Eli Oxenhorn Family Limited
                  Partnership

            (b)   Percent of Class: 0.7%

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

                  (i)   sole power to vote or to direct the vote: 306,077(2)
                        shares

                  (ii)  shared power to vote or to direct the vote: 0 shares

                  (iii) sole power to dispose or to direct the disposition of:
                        306,077(2) shares

                  (iv)  shared power to dispose or to direct the disposition of:
                        0 shares

Instruction: For computations regarding securities which represent a right to
acquire an underlying security see Rule 13d-3(d)(1).

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

            If this statement is being filed to report the fact that as of the
date hereof the reporting person has ceased to be the beneficial owner of more
than five percent of the class of securities, check the following.

Instruction: Dissolution of a group requires a response to this item.

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.

            Not Applicable.

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

            Exhibit A, Joint Filing Agreement, was previously filed with
Schedule 13G, dated August 22, 2001.

Item 9. Notice of Dissolution of Group.

            Not Applicable.


                                  Page 6 of 8


CUSIP NO. 306137100

Item 10. Certification.

            (b)   The following certification shall be included if the statement
                  is filed pursuant to ss.240.13d-1(c):

                  By signing below each party certifies that, to the best of
                  his/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.


                                  Page 7 of 8


CUSIP NO. 306137100

                                    SIGNATURE

      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.

Date: February 13, 2004

                                        /s/ Eli Oxenhorn
                                        ----------------------------------------
                                        Eli Oxenhorn


                                        Eli Oxenhorn Family Limited Partnership

                                        By: /s/ Eli Oxenhorn
                                            ------------------------------------
                                            Name: Eli Oxenhorn
                                            Title: General Partner

Attention: Intentional misstatements or omissions of fact constitute Federal
           criminal violations (See 18 U.S.C. 1001).


                                  Page 8 of 8