FalconStor Software (FALC) 10-Q 2004 Q2 Quarterly report

                                                                    Exhibit 32.1


                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER

  Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C.ss.1350)

            Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C.
ss. 1350), the undersigned,  ReiJane Huai, Chief Executive Officer of FalconStor
Software, Inc., a Delaware Corporation (the "Company"),  does hereby certify, to
his knowledge, that:

            The  Quarterly  Report on Form 10-Q for the  quarter  ended June 30,
2004 of the Company (the  "Report")  fully  complies  with the  requirements  of
Sections  13(a)  and  15(d) of the  Securities  Exchange  Act of  1934,  and the
information  contained in the Report fairly presents,  in all material respects,
the financial condition and results of operations of the Company.



                                         /s/ ReiJane Huai
                                         ----------------
                                         ReiJane Huai
                                         Chief Executive Officer
                                         August 9, 2004