<PAGE>   1
 
                                                                    EXHIBIT 4
 
                          THIRD AGREEMENT OF AMENDMENT
 
     This THIRD Agreement of Amendment ("Amendment") is executed at Cleveland,
Ohio as of October 25, 1996 by and among THE STANDARD PRODUCTS COMPANY (the
"Borrower") and NATIONAL CITY BANK ("National City"), as agent (the "Agent") for
itself, KEYBANK NATIONAL ASSOCIATION (formerly known as SOCIETY NATIONAL BANK
("KeyBank")), COMERICA BANK ("Comerica") and NBD BANK (formerly known as NBD
BANK, N.A.) ("NBD") (hereafter collectively referred to as "Banks").
 
     WHEREAS, Borrower, Banks and Agent entered into a credit agreement dated as
of January 19, 1993 as amended by an Agreement of Amendment dated April 30, 1994
and by an Agreement of Amendment dated August 25, 1995 (the "Agreement") wherein
Banks agreed to make revolving loans to Borrower, under certain terms and
conditions, aggregating not more than the principal amount of One Hundred
Seventy-five Million Dollars ($175,000,000), which amount was reduced on June
30, 1993 to One Hundred Twenty-five Million Dollars ($125,000,000) and which may
be reduced from time to time under the Agreement; and
 
     WHEREAS, Borrower, Banks and Agent want to make certain changes in and to
the Agreement;
 
     NOW, THEREFORE, Borrower, Banks and Agent agree as follows:
 
     1. Section 1.01 (captioned "Certain Defined Terms") is hereby amended such
that the definitions of "Revolving Credit Termination Date" and "Reduction
Standard" shall now read as follows:
 
          "Revolving Credit Termination Date" means January 18, 1999, as the
     same may be extended pursuant to Section 2.02(k), or the earlier date of
     the termination in whole of the aggregate amount of the Revolving Credit
     Commitments pursuant to Section 2.04 or 6.02.
 
          "Reduction Standard" means any one of the standards identified as
     Reduction Standard I, II, III or IV in Schedule 2.06(b) hereto.
 
     2. Section 2.05(a) captioned "Revolving Credit Commitment Fee" is hereby
amended in its entirety to read as follows:
 
          (a) Revolving Credit Commitment Fee. The Borrower agrees to pay to the
     Agent for the account of each Bank a commitment fee on the average daily
     unused portion of such Bank's Revolving Credit Commitment from the date of
     execution of this Agreement until the Revolving Credit Termination Date at
     the rate per annum as shown in the following schedule.
 
<TABLE>
<CAPTION>
                                                                             THEN THE
                              IF THE LEVERAGE IS                         COMMITMENT FEE IS
        --------------------------------------------------------------   -----------------
        <S>                                                              <C>
        Greater than or equal to 45%..................................           1/4%
        Greater than or equal to 40% but less than 45%................           1/4%
        Greater than or equal to 35% but less than 40%................          3/16%
        Less than 35%.................................................          3/16%
</TABLE>
 
     The commitment fee shall be payable on the first day of each January,
     April, July and October during the term of such Bank's Revolving Credit
     Commitment, commencing January 1, 1997, and on the Revolving Credit
     Termination Date.
 
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<PAGE>   2
 
     3. Schedule 2.06(b) is hereby amended in its entirety to read as follows:
 
                                SCHEDULE 2.06(B)
 
<TABLE>
<CAPTION>
                                                            AND THE EBIT RATIO IS        AND THE EBIT RATIO IS
                                          IF THE         GREATER THAN OR EQUAL TO 3.0     LESS THAN 3.0 TO 1.0
                                         LEVERAGE        TO 1.0 THEN THE EUROCURRENCY           THEN THE
  REDUCTION STANDARD APPLICABLE             IS                    MARGIN IS              EUROCURRENCY MARGIN IS
----------------------------------   -----------------   ----------------------------    ----------------------
<S>                                  <C>                 <C>                             <C>
   I..............................   Greater than or           .75%                          .875%
                                     equal to 45%
   II.............................   Greater than or           .625%                          .75%
                                     equal to 40% but
                                     less than 45%
   III............................   Greater than or           .50%                          .625%
                                     equal to 35% but
                                     less than 40%
   IV.............................   Less than to 35%          .375%                          .50%
</TABLE>
 
     4. Subsection 5.05(d) (captioned "Current Ratio") is hereby amended in its
entirety to read as follows:
 
          "5.05(d) Current Ratio. The Borrower will not suffer or permit the
     Current Assets of the Borrower and its Subsidiaries at any time to fall
     below an amount equal to one hundred percent (100%) of the Current
     Liabilities of the Borrower and its Subsidiaries, all as determined on a
     consolidated basis."
 
     5. In all other respects the credit agreement shall remain in full effect.
 
     6. Upon the execution and delivery of this Amendment, the Borrower will not
be in default under the Agreement as so amended.
 
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<PAGE>   3
 
     IN WITNESS WHEREOF, Borrower, Banks and Agent have executed this Third
Agreement of Amendment at the time and place first above mentioned.
 
                                          NATIONAL CITY BANK, AS AGENT
 
                                          By: /s/ TIMOTHY J. LATHE
                                              ----------------------------------
 
                                          Title: SVP
                                                 -------------------------------
 
                                          NATIONAL CITY BANK
 
                                          By: /s/ TIMOTHY J. LATHE
                                              ----------------------------------
 
                                          Title: SVP
                                                 -------------------------------
 
                                          COMERICA BANK
 
                                          By: /s/ MICHAEL SHEA
                                              ----------------------------------
 
                                          Title: Vice President
                                                 -------------------------------
 
                                          THE STANDARD PRODUCTS COMPANY
 
                                          By: /s/ CHARLES F. NAGY
                                              ----------------------------------
 
                                          Title: Treasurer
                                                --------------------------------
 
                                          NBD BANK
 
                                          By: /s/ TERESA A. KALIL
                                              ----------------------------------
 
                                          Title: Vice President
                                                --------------------------------
 
                                          KEYBANK NATIONAL ASSOCIATION
 
                                          By: /s/ THOMAS CRANDELL
                                              ----------------------------------
 
                                          Title: Assistant Vice President
                                                 -------------------------------
 
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