<PAGE>   1
                                                                   Exhibit 10.31



                                 AMENDMENT NO. 1
                            TO CODE SHARING AGREEMENT

     CONTINENTAL AIRLINES, INC. ("Continental") and AMERICA WEST AIRLINES, INC.
("America West") are each party to the Code Sharing Agreement dated June 29,
1994 (the "'Agreement"). America West and Continental each desire to amend the
Agreement as provided below. This amendment is made this 19th day of October,
1998.

     NOW, THEREFORE, IT IS AGREED:

     1. Capitalized terms used herein that are not defined shall have the same
meaning set forth for them in the Agreement. Except as specifically amended and
modified hereby, the Agreement shall remain in effect as written.

     2. The Agreement shall be amended as follows:

        (a) Schedule 1 of the Agreement is hereby replaced in its entirety by
the Schedule 1-A and Schedule 1-B attached hereto to designate the Shared Code
Segments now operated pursuant to the Agreement and to add a list of new Shared
Code Segments to be added to the Agreement effective October 25, 1998 pursuant
to Section 1 of the Agreement or, with respect to international Shared Code
Segments, as soon as reasonably practicable after all applicable regulatory
approvals are obtained for the applicable Shared Code Segment and both parties
have satisfactorily implemented mutually acceptable procedures with respect to
codesharing on such international Shared Code Segments.

        (b) A new sentence shall be added to the end of Clause 1 of the
            Agreement:

        "Either party may, at its own discretion, by thirty (30) days prior
        written notice to the other party, remove a Shared Code Segment
        designated as "New" on Schedules 1-A and 1-B from Schedule 1-A or
        Schedule 1-B, for all purposes of this Agreement."

        (c) A new Clause 9(c) shall be added as follows:

        "Neither CAL nor AWA shall display the designator code of the
        non-operating carrier on any Shared Code Segment which, when AWA is the
        non-operating carrier, does not connect with a flight to or from
        Phoenix, Columbus or Las Vegas, or, when CAL is the non-operating
        carrier, Houston, Newark or Cleveland, except CAL and AWA shall display
        the designator code of the non-operating carrier on any Shared Code
        Segment operated by both CAL and AWA."

        (d) Clause 20 of the Agreement shall be amended by adding the words "and
Amendment No. 1" after the word "Agreement" in the first and second sentences.

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<PAGE>   2
3. Clauses 3, 20, 21, 22, 25 and 26 of the Agreement are herein incorporated by
reference, mutatis mutandis.

CONTINENTAL AIRLINES, INC.                           AMERICA WEST AIRLINES, INC.



By:    /s/ Thomas Barber                           By:     /s/ Bernard Han
       -----------------------------                       ---------------------

Title: VP Alliance Operations                       Title: SVP Planning



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<PAGE>   3
                                                                    SCHEDULE 1-A


                                   HP* FLIGHTS
<TABLE>
<CAPTION>
 CURRENT SEGMENTS                                     NEW SEGMENTS
SEGMENT     IMPLEMENTATION DATE                    SEGMENT     SEGMENT
<S>         <C>                                    <C>         <C>
ABQ-IAH          2/15/95                           ABE-CLE     CLE-YYZ
AUS-IAH          2/15/95                           ACT-IAH     CLL-IAH
BRO-IAH          2/15/95                           ALB-EWR     CLT-IAH
CLE-DEN          10/1/94                           ATL-IAH     CVG-IAH
CLE-IAH          10/1/94                           BDL-CLE     DCA-IAH
CMH-EWR          10/1/94                           BDL-EWR     DUB-EWR
CMH-IAH          10/1/94                           BLD-IAH     DUS-EWR
CRP-IAH          2/15/95                           BGR-EWR     EWR-FRA
DTW-IAH          2/15/95                           BHM-IAH     EWR-GLA
ELP-IAH          2/15/95                           BHX-EWR     EWR-MAN
EWR-LAS           4/2/95                           BNA-IAH     EWR-MDT
EWR-ORF          2/15/95                           BTR-IAH     EWR-MHT
EWR-PHX          10/1/94                           BTV-EWR     EWR-PHL
EWR-PVD          2/15/95                           BUF-CLE     EWR-RIC
EWR-PWM          2/15/95                           BUF-EWR     EWR-ROC
FLL-IAH          10/1/94                           BWI-CLE     EWR-SNN
GSO-IAH          2/15/95                           CAK-CLE     EWR-SYR
HNL-LAX          1/19/96                           CDG-EWR     EWR-YOW
HRL-IAH          2/15/95                           CDG-JAH     EWR-YUL
IAH-IND          10/1/94                           CLE-CMH     EWR-YYZ
IAH-JAX          10/1/94                           CLE-CVG     HOU-IAH
IAH-LAS          10/1/94                           CLE-DCA     IAD-IAH
IAH-LIT          2/15/95                           CLE-DTW     IAH-ILE
IAH-MCO          10/1/94                           CLE-FNT     IAH-JAN
IAH-MFE          2/15/95                           CLE-IAD     IAH-LGA
IAH-MIA          10/1/94                           CLE-LAN     IAH-MEM
IAH-MSY          10/1/94                           CLE-LEX     IAH-MLU
IAH-PBI          10/1/94                           CLE-LGA     IAH-MOB
IAH-PHL          2/15/95                           CLE-MBS     IAH-RDU
IAH-PHX          10/1/94                           CLE-MDT     IAH-SHV
IAH-PIT          10/1/94                           CLE-PHL     IAH-SJO
IAH-PNS          2/15/95                           CLE-PIT     IAH-SJU
IAH-RSW          2/15/95                           CLE-RIC     IAH-TYR
IAH-SDF          2/15/95                           CLE-ROC     IAH-YYZ
IAH-TPA          10/1/94                           CLE-SBN
IAH-TUS          10/1/94                           CLE-SYR
</TABLE>



                                       i.
<PAGE>   4
                                                                    SCHEDULE 1-B



                         CO* FLIGHTS
<TABLE>
<CAPTION>
                 CURRENT SEGMENTS                                 NEW SEGMENT
SEGMENT        IMPLEMENTATION DATE        REINSTATE DATE           SEGMENT
 <S>            <C>                        <C>                    <C>
 BUR-LAS              10/1/94                                       PHX-PSP
 BUR-PHX              10/1/94
 CMH-LAS              10/1/94
 DEN-PHX              10/1/94
 LAS-LAX               1/8/96
 LAS-MDW               2/1/95
 LAS-OAK              10/1/94
 LAS-ONT              10/1/94
 LAS-PDX              10/1/94
 LAS-RNO              10/1/94
 LAS-SAN              10/1/94
 LAS-SEA              10/1/94
 LAS-SFO              10/1/94
 LAS-SLC               2/1/95                   4/6/97
 LAS-SMF              10/1/94
 LAS-TUS              10/1/94
 LAX-PHX               1/8/96
 LGB-PHX              10/1/94
 MCO-PHX               2/1/95                   4/6/97
 OAK-PHX              10/1/94
 ONT-PHX              10/1/94
 PDX-PHX              10/1/94
 PHX-RNO              10/1/94
 PHX-SAN              10/1/94
 PHX-SEA              10/1/94
 PHX-SFO              10/1/94
 PHX-SJC              10/1/94
 PHX-SLC               2/1/95                   4/6/97
 PHX-SMF              10/1/94
 PHX-TUS              10/1/94
 EWR-LAS               4/2/95
 EWR-PHX              10/1/94
 CMH-EWR              10/1/94
 IAH-LAS              10/1/94
 IAH-PHX              10/1/94
</TABLE>


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