<PAGE>   1
                                                                Exhibit 10.10(d)

                            SUPPLEMENTAL TERMS LETTER


As of January 3, 1997

International Remote Imaging Systems, Inc.
9162 Eton Avenue
Chatsworth, CA 91311

Attention: Martin S. McDermut, Vice President, Finance & Administration & CFO

         RE:      CHANGE IN TERMS AGREEMENT ("CHANGE IN TERMS AGREEMENT") DATED
                  AS OF JANUARY 3, 1997, RELATING TO A PROMISSORY NOTE (THE
                  "NOTE") IN THE ORIGINAL PRINCIPAL AMOUNT OF $1,500,000.00
                  EXECUTED BY INTERNATIONAL REMOTE IMAGING SYSTEMS, INC., A
                  DELAWARE CORPORATION ("BORROWER") IN FAVOR OF CITY NATIONAL
                  BANK, A NATIONAL BANKING ASSOCIATION ("CNB")

Dear Mr. McDermut:

         This is to confirm that CNB will extend the credit facility more
completely described in the enclosed Note, subject to the additional terms and
conditions set forth herein and in the Change in Terms Agreement. Capitalized
terms not defined in this letter have the meanings given them in the Note. This
letter is hereby incorporated into the Note (this letter, the Note, the Terms
Letter and in the Change in Terms Agreement, collectively, the "Note").

         NOW, THEREFORE, the parties agree as follows:

1.       DEFINITIONS. Capitalized terms used in this Amendment without 
definition shall have the meanings set forth in the Supplemental Terms Letter
dated July 29, 1996 related to the Note ("Terms Letter").

2.       AMENDMENTS.  The Terms Letter is amended as follows:

         2.1      Section 2. of the Terms Letter is hereby deleted in its 
entirely, and shall be added and inserted a new Section 2. as follows:

                  "2.      Failure of Borrower to furnish CNB, within the times
                           specified, the following statements:

                           2.1      Within forty-five (45) days after the end of
                                    each monthly accounting period of each
                                    fiscal year, a financial statement
                                    consisting of not less than a balance sheet
                                    and income


<PAGE>   2


Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 2


                                    statement, prepared in accordance with
                                    generally accepted accounting principles
                                    consistently applied, which financial
                                    statement may be internally prepared;

                           2.2      Within sixty (60) days after the end of each
                                    quarterly accounting period of each fiscal
                                    year, a financial statement consisting of
                                    not less than a Form 10-Q.;

                           2.3      Within ninety (90) days after the close of
                                    each fiscal year, a copy of the annual
                                    report, on Form 10-K for such year for
                                    Borrower and the Subsidiaries; and

                           2.4      Such additional information, reports and/or
                                    statements as CNB may, from time to time,
                                    reasonably request;"


         2.2      Section 3. of the Terms Letter is hereby deleted in its 
entirely, and shall be added and inserted a new Section 3. as follows:

                  "3.      Failure of Borrower to maintain the following:

                           3.1      Tangible Net Worth plus Subordinated Debt of
                                    not less than the following amounts as of
                                    the stated effective date;

<TABLE>
<CAPTION>
                                       Effective Date           Minimum Amount
                                       --------------          ----------------
<S>                                                            <C>
                                         3/31/97               $  (1,300,000.00)
                                         6/30/97               $  (1,000,000.00)
                                         9/30/97               $    (750,000.00)
                                        12/31/97               $     (50,000.00)
                                         3/31/98               $     550,000.00

</TABLE>
                           3.2      A ratio of Total Senior Liabilities to
                                    Tangible Net Worth plus Subordinated Debt of
                                    not more than 21.50 to 1 as of March 31,
                                    1998;


<PAGE>   3


Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 3


                           3.3      A ratio of Current Assets to Current
                                    Liabilities of not less than the following
                                    amounts as of the stated effective date; and
<TABLE>
<CAPTION>

                                    Effective Date             Minimum Ratio
                                    --------------             -------------
<S>                                                            <C>
                                       3/31/97                   0.76 to 1
                                       6/30/97                   0.76 to 1
                                       9/30/97                   0.77 to 1
                                      12/31/97                   0.83 to 1
                                       3/31/98                   0.87 to 1
</TABLE>


                           3.4      A ratio of Cash Flow from Operations to Debt
                                    Service of not less than the following
                                    amounts as of the stated effective date.

<TABLE>
<CAPTION>
                                    Effective Date             Minimum Ratio
                                    --------------             -------------
<S>                                                            <C>
                                        3/31/97                  0.60 to 1
                                        6/30/97                  0.90 to 1
                                        9/30/97                  1.00 to 1
                                       12/31/97                  1.25 to 1
                                        3/31/98                  1.25 to 1"
</TABLE>

         2.3      Section 4. of the Terms Letter is hereby deleted in its 
entirely, and there shall be added and inserted a new Section 4. as follows:

                  "4.      Failure of Borrower within five (5) days after
                           execution and delivery of this Supplemental Terms
                           Letter to grant CNB a duly perfected security
                           interest, with the exception of the existing TOA
                           lien, in all patents, copyrights and trademarks held
                           by borrower."

         2.4      There shall be added and inserted a definition as follows:

                  "DEBT SERVICE" shall mean (a) the $1,200,000.00 annual
                  principal payments under the Amended and Restated Note dated
                  January 3, 1997 in the original principal amount of
                  $4,900,000.00, prorated per the appropriate period, plus (b)
                  all interest incurred on borrowed money during the twelve
                  month period ending on the date of determination."


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Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 4



         2.5      The definition "TANGIBLE NET WORTH" contained in the Terms 
Letter is hereby deleted in its entirely, and there shall be added and inserted
a definition as follows:

                  "TANGIBLE NET WORTH" shall mean the total of all assets
                  appearing on a balance sheet prepared in accordance with
                  generally accepted accounting principles consistently applied
                  for Borrower and the Subsidiaries on a consolidated basis,
                  minus (a) all intangible assets, including, without
                  limitation, unamortized debt discount, affiliate, employee and
                  officer receivables or advances, goodwill, research and
                  development costs, patents, trademarks, the excess of purchase
                  price over underlying values of acquired companies, any
                  covenants not to compete, deferred charges, copyrights,
                  franchises and appraisal surplus; minus (b) all obligations
                  which are required by generally accepted accounting principles
                  consistently applied to be reflected as a liability on the
                  consolidated balance sheet of Borrower and the Subsidiaries;
                  minus, (c) the amount, if any, at which shares of stock of a
                  non-wholly owned Subsidiary appear on the asset side of
                  Borrower's consolidated balance sheet, as determined in
                  accordance with generally accepted accounting principles
                  consistently applied; minus (d) minority interests; and minus
                  (e) deferred income and reserves not otherwise reflected as a
                  liability on the consolidated balance sheet of Borrower and
                  the Subsidiaries."

         2.6      There shall be added and inserted a definition as follows:

                  "CASH FLOW FROM OPERATIONS" shall be determined on a
                  consolidated basis for Borrower and the Subsidiaries and shall
                  mean the sum of (a) net income after taxes earned, plus (b)
                  amortization of intangible assets, plus (c) interest expense,
                  plus (d) depreciation expensed, plus (e) any other non-cash
                  charges, in each case, as adjusted for (f) change in deferred
                  taxes."

3.       EXISTING AGREEMENTS.  Except as expressly amended herein, the Terms 
Letter shall remain in full force and effect, and in all other respects is
affirmed.

4.       COUNTERPARTS. This Amendment may be executed in any number of 
counterparts, and all such counterparts taken together shall be deemed to
constitute one and the same instrument.


<PAGE>   5


Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 5


5.       GOVERNING LAW.  This Amendment and the rights and obligations of the 
parties hereto shall be construed in accordance with, and governed by the laws
of the State of California.


         IN WITNESS WHEREOF, the parties have executed this Amendment as of the
day and year first above written.


"Borrower"                   INTERNATIONAL REMOTE IMAGING SYSTEMS, INC.,
                             a Delaware corporation


                             By: /s/ Martin S. McDermut
                                 --------------------------
                                 Martin S. McDermut, Vice President,
                                 Finance and Administration/CFO


"CNB"                        CITY NATIONAL BANK, a national
                             banking association


                             By: /s/ Charles Solomon
                                 --------------------------
                                 Charles Solomon, Senior Vice
                                 President/Manager


                             By: /s/ Bruce E. Corey
                                 --------------------------
                                 Bruce E. Corey, Vice President