<PAGE>
 
                                                           Exhibit 10.10 (b)(ii)

                                                                  CONFORMED COPY

                 AMENDMENT NO. 1 TO FIVE-YEAR CREDIT AGREEMENT


     AMENDMENT dated as of January 7, 1998 to the Five-Year 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

     (ii) "one month or not less than 30 days" in Exhibit D.
<PAGE>
 
     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/ James E. Condon
                                                   -----------------------------
                                                   Title:  Vice President


                                              CO-ARRANGERS
                                              ------------
                                              BANK OF AMERICA NATIONAL TRUST
                                                  AND SAVINGS ASSOCIATION


                                              By:  /s/ Craig S. Munro
                                                   -----------------------------
                                                   Title:  Managing Director

                                       2
<PAGE>

                                          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/ Hajime Watanabe
                                               -----------------------------
                                               Title: Deputy 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/ John L. Church
                                       --------------------------------------
                                       Title:  Vice President


                                  By:  /s/ Angela Reitz
                                       --------------------------------------
                                       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


                                  SOCIETE GENERALE

                                       4
<PAGE>
 
                                  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/ Gordon R. Holtby
                                       --------------------------------------
                                       Title:  Vice President and 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