Exhibit (3b)



                            CERTIFICATE OF AMENDMENT

                     OF THE CERTIFICATE OF INCORPORATION OF

                                   UNIFI, INC.

                UNDER SECTION 805 OF THE BUSINESS CORPORATION LAW


         The undersigned, Vice President and Secretary of Unifi, Inc., hereby
certifies:

         1. The name of the corporation is UNIFI, INC. (the corporation was
originally named Automated Environmental Systems, Inc.).

         2. A Certificate of Incorporation of Unifi, Inc. was filed by the
Department of State on the 18th day of January, 1969 under the name Automated
Environmental Systems, Inc. A Restated Certificate of Incorporation of Unifi,
Inc. was filed by the Department of State on the 6th day of November, 1990, a
Certificate of Amendment was filed by the Department of State on the 13th day of
November, 1991, a Certificate of Amendment was filed by the Department of State
on the 20th day of January, 1994, and a Restated Certificate of Incorporation of
Unifi, Inc. was filed by the Department of State on the 9th day of September,
1994.

         3. The Restated Certificate of Incorporation of this Corporation is
hereby amended to declassify the Board of Directors of the Corporation, and in
relation thereto ARTICLE SEVENTH of the Restated Certificate of Incorporation is
hereby deleted in its entirety and a new ARTICLE SEVENTH is hereby inserted to
henceforth read as follows:

         "SEVENTH: The number of Directors shall be fixed in the By-Laws but in
         no case shall be less than nine (9), but this number may be increased
         and subsequently increased or decreased from time to time by the
         affirmative vote of the majority of the Board, except that the number
         of Directors shall not be less than nine (9). A Director shall hold
         office until his successor shall be elected and qualified, subject to
         prior death, resignation, retirement, or removal from office.





         Newly created directorships resulting from an increase in the number of
         Directors and vacancies caused by death, resignation, retirement or
         removal from office, may be filled by the vote of a majority of the
         Directors remaining in office. Any Director elected by the Board to
         fill a vacancy shall serve until the next meeting of the Shareholders,
         at which the election of Directors is in the regular order of business,
         and until his successor is elected and qualified. In no case will a
         decrease in the number of Directors shorten the term of an incumbent
         Director."


         4. The foregoing amendment to the Restated Certificate of Incorporation
of this Corporation was authorized by the Board of Directors of the Corporation
on the 4th day of July, 2002, and adopted by the affirmative vote of a majority
of the shares of Unifi, Inc.'s common stock entitled to notice of and to vote at
the Annual Meeting of the Shareholders held on October 23, 2002, a quorum having
been present.

         IN WITNESS WHEREOF, this Certificate has been subscribed this the
6th day of January, 2003, by the undersigned, who affirmed that the
statements made herein are true under penalties of perjury.

                                           UNIFI, INC.


                                           CHARLES F. MCCOY
                                           -------------------------------------
                                           Charles F. McCoy
                                           Vice President & Secretary


[CORPORATE SEAL]










                                AMENDMENT TO THE

                          CERTIFICATE OF INCORPORATION

                                       OF

                                   UNIFI, INC.



                UNDER SECTION 805 OF THE BUSINESS CORPORATION LAW









                                                     FILED BY:

                                                               CHARLES F. MCCOY
                                                          VICE PRESIDENT & SEC.
                                                                 OF UNIFI, INC.
                                                                 P.O. BOX 19109
                                                     GREENSBORO, NC  27419-9109
                                                                (336)  316-5660