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), the undersigned,  ReiJane Huai, Chief Executive Officer of FalconStor
Software, Inc., a Delaware Corporation (the "Company"),  does hereby certify, to
his knowledge, that:

            The Annual  Report on Form 10-K for the fiscal  year ended  December
31, 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
                                                March 16, 2005