<PAGE>
 
                                       January 30, 1997
                                                                    Exhibit 10.7

Allegiance Corporation
1430 Waukegan Road
McGaw Park, Illinois 60085

     Re:  First Amendment to Credit Agreement
          -----------------------------------

Ladies/Gentlemen:

     Please refer to the Facility A Credit Agreement (the "Credit Agreement") 
dated as of September 23, 1996 among Allegiance Corporation (the "Company"), 
various Banks, The First National Bank of Chicago, as Syndication Agent, 
NationsBank of Texas, N.A., as Documentation Agent, Morgan Guaranty Trust 
Company of New York, as Syndication Agent, and Bank of America National Trust 
and Savings Association, as Administrative Agent.  Capitalized terms used 
herein and not otherwise defined herein shall have the meanings assigned thereto
in the Credit Agreement.

     The Company, the Agents and the Banks agree that the definition of 
"Extraordinary Items" in Section 7.01(i) of the Credit Agreement is amended by 
deleting the amounts "$50,000,000" therein and substituting the amount 
"$100,000,000" therefor.

     Except as amended above, all terms and provisions of the Credit Agreement 
shall remain in full force and effect and are hereby ratified and confirmed in 
all respects.

     This letter amendment shall become effective when the Administrative Agent 
has received counterparts hereof signed by the Company and the Majority Banks.

     This letter amendment shall be deemed to be a contract made under the laws 
of the State of Illinois, and for all purposes shall be construed in accordance 
with the laws of the State of Illinois, without regard to the principles of 
conflicts of laws.

     Please evidence your agreement to the foregoing by signing and returning a 
counterpart of this letter amendment.
<PAGE>
 
                                       BANK OF AMERICA NATIONAL TRUST
                                       AND SAVINGS ASSOCIATION,
                                       as Administrative Agent

                                       By:_________________________________
                                             Title:


                                       BANK OF AMERICA ILLINOIS,
                                       individually and as Swing-Line Bank

                                       By:_________________________________
                                             Title:


                                       THE FIRST NATIONAL BANK OF CHICAGO,
                                       individually and as Syndication Agent
                                       and Co-Arranger

                                       By:_________________________________
                                             Title:


                                       MORGAN GUARANTY TRUST COMPANY
                                       OF NEW YORK,
                                       individually and as Co-Syndication Agent
                                       and Co-Arranger

                                       By:_________________________________
                                             Title:


                                       NATIONSBANK OF TEXAS, N.A.,
                                       individually and as Documentation Agent
                                       and Co-Arranger

                                       By:_________________________________
                                             Title:


                                       THE CHASE MANHATTAN BANK,
                                       individually and as Co-Agent

                                       By:_________________________________
                                             Title:


                                      -2-
<PAGE>

 
                                       CREDIT LYONNAIS CHICAGO BRANCH,
                                        individually and as Co-Agent
                                                
                                       By:
                                           -------------------------------------
                                           Title:

 
                                       CREDIT SUISSE, individually and 
                                        as Co-Agent
                                                
                                       By: 
                                           -------------------------------------
                                           Title:
    
                                       By: 
                                           -------------------------------------
                                           Title:

                                       DEUTSCHE BANK AG
                                        CHICAGO AND/OR CAYMAN ISLANDS
                                        BRANCHES, individually and
                                        as Co-Agent
                                                
                                       By:
                                           -------------------------------------
                                           Title:

                                       By:
                                           -------------------------------------
                                           Title:

 
                                       THE SUMITOMO BANK, LIMITED,
                                        CHICAGO BRANCH
                                        individually and as Co-Agent
                                                
                                       By:
                                           -------------------------------------
                                           Title:

 
                                       TORONTO DOMINION (TEXAS), INC.,
                                        individually and as Co-Agent
                                                
                                       By:
                                           -------------------------------------
                                           Title:
 

                                      -3-

<PAGE>
 
                                       THE BANK OF TOKYO-MITSUBISHI, LTD.
                                         CHICAGO BRANCH


                                       By:_______________________________
                                          Title:

                                       CITIBANK, N.A.


                                       By:_______________________________ 
                                          Title: 

                                       CAISSE NATIONALE DE CREDIT
                                         AGRICOLE


                                       By:_______________________________
                                          Title:

                                       THE FUJI BANK, LIMITED


                                       By:_______________________________
                                          Title:

                                       THE INDUSTRIAL BANK OF JAPAN, LIMITED
                                         CHICAGO BRANCH


                                       By:_______________________________
                                          Title:

                                       MELLON BANK, N.A.


                                       By:_______________________________
                                          Title:

                                       THE NORTHERN TRUST COMPANY


                                       By:_______________________________
                                          Title:


                                      -4-
<PAGE>
 
                                    PNC BANK, NATIONAL ASSOCIATION



                                    By:_______________________________
                                       Title:

                                    UNION BANK OF SWITZERLAND,
                                      NEW YORK BRANCH



                                    By:_______________________________
                                       Title:

                                    By:_______________________________
                                       Title:

                                    WACHOVIA BANK OF GEORGIA, N.A.


                                    By:_______________________________
                                       Title:

                                    WELLS FARGO BANK, N.A.


                                    By:_______________________________
                                       Title: 

Accepted and Agreed                 By:_______________________________
as of January 30, 1997:                Title: 

ALLEGIANCE CORPORATION


By:_______________________________
   Title:


                                      -5-