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                                                                    Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO SECTION
906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Possis Medical, Inc. (the "Company") on
Form 10-K for the year ended July 31, 2007, as filed with the Securities and
Exchange Commission on the date hereof (the "Report"), I, Robert G. Dutcher,
Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section
1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002,
that:

1.   The Report fully complies with the requirements of Section 13(a) or 15(d)
     of the Securities Exchange Act of 1934; and

2.   The information contained in the Report fairly presents, in all material
     respects, the financial condition and results of operations of the Company.

October 12, 2007                                /s/   Robert G. Dutcher
                                           -------------------------------------
                                           Robert G. Dutcher
                                           Chief Executive Officer

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