Exhibit 32.1

Certification pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley act of 2001.

In connection with the Quarterly Report Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 on Form 10-QSB of Non-Invasive Monitoring Systems, Inc. (the “Company”) for the period ended October 31, 2003, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Marvin A Sackner, M.D., Principal Executive Officer of the Company, certify, pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2001, that:

The Report fully complies with the requirements of Section 13(a) or 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.

Dated: December 5, 2003

/s/    Marvin A Sackner, M.D.         

Marvin A Sackner, M.D.