UNIFI INC
SC 13G/A, 1997-02-14
TEXTILE MILL PRODUCTS
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<PAGE>   1

                     SECURITIES AND EXCHANGE COMMISSION
                           Washington, D.C. 20549

                                SCHEDULE 13G

                  Under the Securities Exchange Act of 1934
                              Amendment No. 6

                             UNIFI INCORPORATED

                                   COMMON

                              CUSIP:  904677101

                              December 31, 1996


    Check the following box if a fee is being paid with this statement _

<TABLE>
            <S>                                                          <C>                <C>
            (1)     Names of Reporting Persons S.S. or I.R.S.            Wachovia Corporation
            Identification Nos. of Above Persons                         56-1473727
            (2)     Check the Appropriate Box if a Member of a           (a)      N/A
            Group (See Instructions)
                                                                         (b)      N/A
            (3)     SEC Use Only
            (4)     Citizenship or Place of Organization                 North Carolina
            Number of Shares Beneficially Owned by Each Reporting
            Person With
                            (5)     Sole Voting Power                                       3,330,525
                            (6)     Shared Voting Power                                     1,176,867
                            (7)     Sole Dispositive Power                                  4,575,393
                            (8)     Shared Dispositive Power                                    1,862
            (9)     Aggregate Amount Beneficially Owned by Each                             4,632,817
            Reporting Person
            (10)    Check if Aggregate Amount in Row 9 Excludes
            Certain Shares (See Instructions)
            (11)    Percent of Class Represented by Amount in Row 9                  7.2%
            (12)    Type of Reporting Person
                    (See Instructions)                                                HC
</TABLE>





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<PAGE>   2


ITEM 7           IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH
                 ACQUIRED THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING
                 COMPANY.

                 The securities to which this report relates are held by
                 Wachovia Bank of North Carolina, NA, Wachovia Bank of Georgia,
                 NA and Wachovia Bank of South Carolina, NA as trustees.  (See
                 Exhibit A.)

                 This filing should not be construed as an admission that the
                 trustees or their parent, Wachovia Corporation, are, for the
                 purposes of Section 13(d) or 13(g) of the Act, beneficial
                 owners of any securities covered by this statement.

ITEM 10          CERTIFICATION:

                 BY SIGNING BELOW, I CERTIFY THAT, TO THE BEST OF MY KNOWLEDGE
                 AND BELIEF, THE SECURITIES REFERRED TO ABOVE WERE NOT ACQUIRED
                 FOR THE PURPOSE OF AND DO NOT HAVE THE EFFECT OF CHANGING OR
                 INFLUENCING THE CONTROL OF THE ISSUER OF SUCH SECURITIES AND
                 WERE NOT ACQUIRED IN CONNECTION WITH OR AS A PARTICIPANT IN
                 ANY TRANSACTION HAVING SUCH PURPOSES OR EFFECT.

                                  SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this statement is true, complete and correct.

DATE:        February 14, 1997

FOR:         Wachovia Corporation


BY:          Ricky B. Nicks
             ----------------------------------------
             Attorney-in-Fact
             Ricky B. Nicks, Executive Vice President
             Wachovia Operational Services Corporation
             (Authorized by Wachovia Corporation under a limited power of
             attorney filed with the Schedule 13G for Equus II, Ltd., CUSIP
             294766100, filed by Wachovia Corporation on February 14, 1997.)

- --------------------------------------------------------------------------------
                                   EXHIBIT A

The following entities agree that this Schedule 13G is filed on their behalf by
the Wachovia Corporation.

<TABLE>
<CAPTION>
                                                       IRS IDENTIFICATION
                    SUBSIDIARY                               NUMBER                         ITEM 3 CLASSIFICATION
 <S>                                                       <C>                <C>
 Wachovia Bank of Georgia, N.A.                            58-0242985         Bank as defined by section 3(a)(6) of the Act
 Wachovia Bank of North Carolina, N.A.                     56-0927594         Bank as defined by section 3(a)(6) of the Act
 Wachovia Bank of South Carolina, N.A.                     57-0539952         Bank as defined by section 3(a)(6) of the Act
</TABLE>





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