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                                                                     EXHIBIT 4.1


                           GALILEO INTERNATIONAL, INC.
                                9700 West Higgins
                               Rosemont, IL 60618


                                  June 15, 2001


LaSalle Bank National Association
Corporate Trust Department
135 S. LaSalle Street, Suite 1960
Chicago, Illinois  60603

Attention: Mark Rimkus


                     Re: Amendment No. 1 to Rights Agreement

Dear Mr. Rimkus:

                  Pursuant to Section 27 of the Rights Agreement (the "Rights
Agreement"), dated as of February 22, 2001, between Galileo International, Inc.
(the "Company"), and LaSalle Bank National Association, as rights agent, the
Company, by resolution adopted by its Board of Directors, hereby amends the
Rights Agreement as follows:

                  1. Section 1(a) of the Rights Agreement is hereby amended and
restated in its entirety as follows:

                  "(a) "Acquiring Person" means any Person (other than the
                  Company or any Related Person) who or which, together with all
                  Affiliates and Associates of such Person, is the Beneficial
                  Owner of 15% or more of the then-outstanding Common Shares;
                  provided, however, that a Person will not be deemed to have
                  become an Acquiring Person solely as a result of a reduction
                  in the number of Common Shares outstanding unless and until
                  such time as (i) such Person or any Affiliate or Associate of
                  such Person thereafter becomes the Beneficial Owner of
                  additional Common Shares, other than as a result of a stock
                  dividend, stock split or similar transaction effected by the
                  Company in which all holders of Common Shares are treated
                  equally, or (ii) any other Person who is the Beneficial Owner
                  of Common Shares thereafter becomes an Affiliate or Associate
                  of such Person; provided further, however, that any Person
                  (other than the Company or any Related Person) that, or which,
                  together with all Affiliates and Associates of such Person,
                  Beneficially Owns 15% or more of the then-outstanding Common
                  Shares as of the date of this Agreement shall not be deemed to
                  have become an Acquiring Person unless and until such time as
                  such Person, together with all Affiliates and Associates of
                  such Person, shall become the Beneficial Owner of 20% or more
                  of the then-outstanding Common Shares; provided further,
                  however, that none of Parent, Purchaser or any of their
                  Affiliates or Associates shall be deemed to have become an
                  Acquiring Person solely as a result of the approval, execution
                  or delivery of the Merger Agreement, the Option Agreement,


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                  the SAir Agreement or the Transaction Support Agreement or the
                  consummation of the transactions contemplated thereby,
                  including without limitation the purchase of Common Shares
                  through the exercise of the Option (as defined in the Option
                  Agreement), unless and until such time as (i) such Person,
                  together with all Affiliates and Associates of such Person,
                  shall become the Beneficial Owner of additional Common Shares
                  other than as a result of a stock dividend, stock split or
                  similar transaction effected by the Company in which all
                  holders of Common Shares are treated equally, or (ii) any
                  other Person who is the Beneficial Owner of Common Shares
                  thereafter becomes an Affiliate or Associate of such Person.
                  Notwithstanding the foregoing, if the Board of the Company
                  determines in good faith that a Person who would otherwise be
                  an "Acquiring Person" as defined pursuant to the foregoing
                  provisions of this paragraph (a), has become such
                  inadvertently and without any intention of changing or
                  influencing control of the Company, and such Person divests as
                  promptly as practicable (as determined by the Board of
                  Directors of the Company) a sufficient number of Common Shares
                  so that such Person would no longer be an "Acquiring Person"
                  as defined pursuant to the foregoing provisions of this
                  paragraph (a), then such Person shall not be deemed to be an
                  "Acquiring Person" for any purposes of this Agreement."

                  2. Section 1(b) of the Rights Agreement is hereby amended and
restated in its entirety as follows:

                  "(b) "Affiliate" and "Associate" will have the respective
                  meanings ascribed to such terms in Rule 12b-2 of the General
                  Rules and Regulations under the Exchange Act, as in effect on
                  the date of this Agreement; provided, however, that a Person
                  will not be deemed to be the Affiliate or Associate of another
                  Person solely because either or both Persons (i) are or were
                  Directors of the Company, (ii) are, as of the date of this
                  Agreement, parties to any of the agreements set forth on
                  Schedule I hereto, each as in effect on the date of this
                  Agreement, without giving effect to any amendment,
                  modification or supplement to such agreements that takes
                  effect after the date of this Agreement, (iii) are, as of June
                  15, 2001, parties to the Transaction Support Agreement,
                  without giving effect to any amendment, modification or
                  supplement to such agreement that takes effect after June 15,
                  2001, or (iv) become parties to the SAir Agreement."

                  3. Section 1(c)(iv) of the Rights Agreement is hereby amended
and restated in its entirety as follows:

                  "(iv) of which any other Person is the Beneficial Owner, if
                  such Person or any of such Person's Affiliates or Associates
                  has any agreement, arrangement or understanding (whether or
                  not in writing) with such other Person (or any of such other
                  Person's Affiliates or Associates) with respect to acquiring,
                  holding, voting or disposing of any securities of the Company;
                  provided, however, that a Person will not be deemed to be the
                  Beneficial Owner or to Beneficially Own securities
                  Beneficially Owned by another Person solely because both
                  Persons (i) are, as of the date of this Agreement, parties to
                  any of the agreements set forth on Schedule I hereto, each as
                  in effect on the date of this Agreement, without giving effect
                  to any amendment, modification or supplement to such
                  agreements that takes effect after the date of this Agreement
                  (ii) are, as of June 15, 2001, parties to the Transaction
                  Support



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                  Agreement, without giving effect to any amendment,
                  modification or supplement to such agreement that takes effect
                  after June 15, 2001, or (iii) become parties to the SAir
                  Agreement."

                  4. Section 1(j) of the Rights Agreement is hereby amended and
restated in its entirety as follows:

                  "(j) "Expiration Date" means the earliest of (i) the Close of
                  Business on the Final Expiration Date, (ii) the time at which
                  the Rights are redeemed as provided in Section 23, (iii) the
                  time at which all exercisable Rights are exchanged as provided
                  in Section 24, and (iv) immediately prior to the Effective
                  Time (as defined in the Merger Agreement)."

                  5. Section 1 of the Rights Agreement is hereby amended by
adding the following new Sections 1(dd), 1(ee), 1(ff) and 1(gg) immediately
after Section 1(cc):

                  "(dd) "Merger Agreement" means the Agreement and Plan of
                  Merger, dated as of June 15, 2001, among the Company, Cendant
                  Corporation, a Delaware corporation ("Parent"), and Galaxy
                  Acquisition Corp., a Delaware corporation ("Purchaser").

                  (ee) "Option Agreement" means the Option Agreement, dated as
                  of June 15, 2001, among the Company and Parent.

                  (ff) "SAir Agreement" means an agreement, document or
                  instrument, and any amendments thereto, the substance and form
                  of which have been approved in writing by an authorized
                  officer of the Company, pursuant to which SAirGroup and any of
                  its Affiliates or Associates (i) grant to Parent a proxy,
                  whether or not irrevocable, to vote Common Shares in favor of
                  the Merger (as defined in the Merger Agreement), and / or (ii)
                  agree to certain transfer restrictions with respect to Common
                  Shares Beneficially Owned by them, and / or (iii) agree to
                  certain non-solicitation obligations.

                  (gg) "Transaction Support Agreement" means the Transaction
                  Support Agreement, dated as of June 15, 2001, among Parent,
                  United Airlines, Inc. and Covia LLC."

                  6. Section 1 of the Rights Agreement is hereby amended by
adding the following new paragraph at the end of that Section:

                           "Notwithstanding anything in this Agreement to the
                  contrary, none of Parent, Purchaser, any of their Affiliates
                  or Associates or any of their permitted assignees or
                  transferees shall be deemed an Acquiring Person and none of a
                  Distribution Date, a Share Acquisition Date, or a Triggering
                  Event shall be deemed to occur or to have occurred, and that
                  the Rights will not become separable, distributable,
                  unredeemable or exercisable, in each such case, solely by
                  reason or solely as a result of (i) the approval, execution,
                  or delivery of the Merger Agreement, the Option Agreement, the
                  SAir Agreement or the Transaction Support Agreement, (ii) the
                  consummation of the Merger (as defined in the Merger
                  Agreement), (iii) the consummation of the other transactions
                  contemplated by the Merger Agreement, the Option Agreement,
                  the SAir



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                  Agreement or the Transaction Support Agreement, or (iv) the
                  announcement of any of the foregoing."

                  7. The Rights Agreement shall not otherwise be supplemented or
amended by virtue of this Amendment No. 1 to the Rights Agreement, but shall
remain in full force and effect.

                  8. Capitalized terms used without other definition in this
Amendment No. 1 to the Rights Agreement shall be used as defined in the Rights
Agreement.

                  9. This Amendment No. 1 to the Rights Agreement will be deemed
to be a contract made under the internal substantive laws of the State of
Delaware and for all purposes will be governed by and construed in accordance
with the internal substantive laws of such State applicable to contracts to be
made and performed entirely within such State.

                  10. This Amendment No. 1 to the Rights Agreement may be
executed in any number of counterparts and each of such counterparts will for
all purposes be deemed to be an original, and all such counterparts will
together constitute but one and the same instrument.

                  11. This Amendment No. 1 to the Rights Agreement shall be
effective as of, and immediately prior to, the execution and delivery of the
Merger Agreement, and all references to the Rights Agreement shall, from and
after such time, be deemed to be references to the Rights Agreement as amended
hereby.

                  12. Exhibits B and C to the Rights Agreement shall be deemed
amended in a manner consistent with this Amendment No. 1 to the Rights
Agreement.

                                          Very truly yours,

                                          GALILEO INTERNATIONAL, INC.


                                          By: /s/ James E Barlett
                                             Name: James E Barlett
                                             Title: Chairman, President & CEO

Accepted and agreed to as of the
effective time specified above:

LaSALLE BANK NATIONAL
ASSOCIATION


By:  /s/ Mark Rimkus
     Name: Mark Rimkus
     Title: Assistant Vice President



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