<PAGE>
 
                                                           Exhibit 10.10 (a)(ii)

                                                                  CONFORMED COPY


                  AMENDMENT NO. 1 TO 364-DAY CREDIT AGREEMENT


     AMENDMENT dated as of December 12, 1997 to the 364-Day Credit Agreement
dated as of July 23, 1997, (the "Credit Agreement") among GALILEO INTERNATIONAL
INC. (the "Borrower"), the BANKS party thereto (the "Banks") and MORGAN GUARANTY
TRUST COMPANY OF NEW YORK, as Agent (the "Agent").

                             W I T N E S S E T H :

     WHEREAS, the parties hereto desire to amend the Credit Agreement to modify
the definition of Interest Period;

     NOW, THEREFORE, the parties hereto agree as follows:

     Section 1.  Defined Terms; References.  Unless otherwise specifically 
defined herein, each term used herein which is defined in the Credit Agreement
has the meaning assigned to such term in the Credit Agreement. Each reference to
"hereof", "hereunder", "herein" and "hereby" and each other similar reference
and each reference to "this Agreement" and each other similar reference
contained in the Credit Agreement shall, after this Amendment becomes effective,
refer to the Credit Agreement as amended hereby.

     Section 2.  Definition of Interest Period.  The definition of "Interest
Period" in Section 1.01 of the Credit Agreement is amended by

     (i)   adding the words "14, 45 or 75 days thereafter or" immediately
following the word "ending" in the third line of clause (3); and

     (ii)  by replacing the number "30" in clause (4) with the number "14."

     SECTION 3. Amendment to Exhibit B and Exhibit D to the Credit Agreement. 
The final footnote to Exhibit B and the third footnote to Exhibit D to the 
Credit Agreement are hereby amended by substituting "14 days" for

     (i)   "one month (LIBOR Auction) or not less than 30 days (Absolute Rate 
Auction)" in Exhibit B; and

<PAGE>
 
     (ii) "one month or not less than 30 days" in Exhibit D.

     Section 4.  Governing Law. This Amendment shall be governed by and
construed in accordance with the laws of the State of New York.

     Section 5.  Counterparts. This Amendment may be signed in any number of
counterparts, each of which shall be an original, with the same effect as if the
signatures thereto and hereto were upon the same instrument.

     Section 6.  Effectiveness. This Amendment shall become effective on the
date when the Agent shall have received from each of the Borrower and the
Required Banks a counterpart hereof signed by such party or facsimile or other
written confirmation (in form satisfactory to the Agent) that such party has
signed a counterpart hereof.

     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed as of the date first above written.

                                       GALILEO INTERNATIONAL, INC.


                                       By:  /s/ Paul H. Bristow
                                            ---------------------------------
                                            Title:  Senior Vice President and
                                                    Chief Financial Officer


                                       AGENT
                                       -----
                                       MORGAN GUARANTY TRUST
                                          COMPANY OF NEW YORK



                                       By:  /s/ Robert Bottamedi
                                            ---------------------------------
                                            Title:  Vice President


                                       CO-ARRANGERS
                                       ------------
                                       BANK OF AMERICA NATIONAL TRUST
                                          AND SAVINGS ASSOCIATION
<PAGE>
 
                         By:/s/ Bridget Garavalia
                            ----------------------------
                            Title:  Managing Director



                         BANK OF MONTREAL



                         By:/s/ Cecily M. Mistarz
                            ----------------------------
                            Title:  Managing Director



                         CO-AGENTS
                         ---------
                         MIDLAND BANK PLC



                         By:/s/ Christopher M. Samms
                            ----------------------------
                            Title:   Corporate Banking Manager



                         THE BANK OF TOKYO-MITSUBISHI,

                            LTD., CHICAGO BRANCH



                         By:/s/ Tokutaro Sekine
                            ----------------------------
                            Title:  General Manager



                         THE SUMITOMO BANK, LIMITED

                            CHICAGO BRANCH



                         By:/s/ John H. Kemper
                            ----------------------------
                            Title:  Senior Vice President

                                       3
<PAGE>
 
                         ABN AMRO BANK N.V.



                         By:/s/ Angela Reitz
                            ----------------------------
                            Title:  Vice President



                         By:/s/ John L. Church
                            ----------------------------
                            Title:  Vice President



                         BANK AUSTRIA AKTIENGESELLSCHAFT,
                            NEW YORK BRANCH



                         By:/s/ J. Anthony Seay
                            ----------------------------
                            Title:  Vice President



                         By:/s/ Karen L. Jill
                            ----------------------------
                            Title: Assistant Vice President



                         PARTICIPANTS
                         ------------
                         CREDIT LYONNAIS
                            NEW YORK BRANCH



                         By:/s/ Philippe Soustra
                            ----------------------------
                            Title:  Senior Vice President



                         ROYAL BANK OF CANADA



                         By:/s/ Brian Bolotin
                            ----------------------------
                            Title:  Manager

                                       4
<PAGE>

                         SOCIETE GENERALE
                            CHICAGO BRANCH


                         By: /s/ Jose A. Moreno
                            ---------------------------------------
                            Title:  Vice President and Team Leader



                         SWISS BANK CORPORATION,
                            STAMFORD BRANCH


                         By: /s/ Reto Jenal
                            ---------------------------------------
                            Title:  Director
                                    Banking Finance


                         By: /s/ Dorothy L. McKinley
                            ---------------------------------------
                            Title:  Associate Director
                                    Banking Products Support, N.A.



                         THE NORTHERN TRUST COMPANY


                         By: /s/ James F. T. Monhart
                            ---------------------------------------
                            Title:  Vice President


                                       5
<PAGE>
 
                         THE SANWA BANK, LIMITED,
                            CHICAGO BRANCH


                         By: /s/ Tomomi Omura
                            ------------------------------------
                            Title:  Assistant General Manager



                         WESTDEUTSCHE LANDESBANK
                            GIROZENTRALE


                         By: /s/ Salvatore Battinelli
                            ------------------------------------
                            Title: Vice President


                         By: /s/ Lisa Walker
                            ------------------------------------
                            Title: Associate



                         THE LONG-TERM CREDIT BANK OF
                            JAPAN, LTD.


                         By: /s/ Armund J. Schoen, Jr.
                            ------------------------------------
                            Title:  Senior Vice President

                                       6
<PAGE>
 
                         MORGAN GUARANTY TRUST
                            COMPANY OF NEW YORK,
                            as Agent


                         By: /s/ James E. Condon
                            -----------------------------
                            Title:  Vice President


















                                       7