Exhibit (32a)


                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 Unifi, Inc. (the "Company") Annual Report on Form 10-K
for the period ended June 29, 2003 as filed with the Securities and Exchange
Commission on the date hereof (the "Report"), I, Brian R. Parke, 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, as
                  amended; and

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



Date:    September 22, 2003            By: /s/  BRIAN R. PARKE
       ----------------------              -------------------------------------
                                           Brian R. Parke
                                           President and Chief Executive Officer





A signed original of this written statement required by Section 906 has been
provided to Unifi, Inc. and will be retained by Unifi, Inc. and furnished to the
Securities and Exchange Commission or its staff upon request.