<PAGE>

                                                                     EXHIBIT 4.1


<PAGE>

                     SECOND AMENDMENT TO RIGHTS AGREEMENT

          SECOND AMENDMENT, dated as of January 23, 2001 ("Second Amendment"),
to Rights Agreement dated as of April 23, 1997 and amended on March 19, 1999
(the "Rights Agreement"), between ResMed Inc. (the "Company"), and American
Stock Transfer & Trust Company (the "Rights Agent"). Capitalized terms used but
not otherwise defined herein shall have the meanings ascribed to them in the
Rights Agreement.

          WHEREAS, the Company and the Rights Agent previously entered into the
Rights Agreement; and

          WHEREAS, pursuant to Section 26 of the Rights Agreement, the Company
and the Rights Agent may from time to time supplement or amend any provision of
the Rights Agreement in accordance with the terms of such Section 26.

          NOW, THEREFORE, in consideration of the foregoing premises and mutual
agreements set forth in this Second Amendment, the parties hereby further amend
the Rights Agreement as follows:

          1.   Section 1.1 of the Rights Agreement is hereby amended and
restated in its entirety as follows:

          "1.1 "Acquiring Person" shall mean any Person (as such term is
     hereinafter defined) who or which, together with all Affiliates and
     Associates (as such terms are hereinafter defined) of such Person, shall be
     the Beneficial Owner (as such term is hereinafter defined) of 20% or more
     of the Common Shares of the Company then outstanding but shall not include
     the Company, any Subsidiary of the Company or any employee benefit plan of
     the Company or of any Subsidiary of the Company or any entity holding
     shares of capital stock of the Company for or pursuant to the terms of any
     such plan, in its capacity as an agent or trustee for any such plan.
     Notwithstanding the foregoing, no Person shall become an "Acquiring Person"
     as the result of an acquisition of Common Shares by the Company which, by
     reducing the number of shares outstanding, increases the proportionate
     number of shares beneficially owned by such Person to 20% or more of the
     Common Shares of the Company then outstanding; provided, however, that if a
     Person shall become the Beneficial Owner of 20% or more of the Common
     Shares of the Company then outstanding solely by reason of share purchases
     by the Company and shall, after such share purchases by the Company, become
     the Beneficial Owner of any additional Common Shares of the Company, then
     such Person shall be deemed to be an "Acquiring Person." Notwithstanding
     the foregoing, if the Board of Directors 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 Section 1.1, has
     become such inadvertently, and such Person divests as promptly as
     practicable a sufficient number of Common Shares so that such Person would
     no longer be an Acquiring Person, as
<PAGE>

     defined pursuant to the foregoing provisions of this Section 1.1, then such
     Person shall not be deemed to be an "Acquiring Person" at any time for any
     purposes of this Agreement."

          2.   Section 1.11 of the Rights Agreement is hereby amended and
restated in its entirety as follows:

          "1.11  A "Trigger Event" shall be deemed to have occurred upon any
     Person becoming an Acquiring Person. Notwithstanding the foregoing, a
     Trigger Event shall not be deemed to have occurred if the event causing the
     20% ownership threshold to be crossed is an acquisition of Common Shares
     made pursuant to a cash tender offer made pursuant to the rules and
     regulations under the Exchange Act and filed with the Securities and
     Exchange Commission on Schedule 14D-1 (or any successor form) for all
     outstanding Common Shares not beneficially owned by the Person making such
     offer (or by its Affiliates or Associates) so long as the Board of
     Directors of the Company determines prior to the time that any Person has
     become an Acquiring Person and, after receiving advice from one or more
     investment banking firms, that such offer is (i) at a price and on terms
     which are fair to stockholders (taking into account all factors which such
     members of the Board deem relevant, including without limitation, prices
     which could reasonably be achieved if the Company or its assets were sold
     on an orderly basis designed to realize maximum value) and (ii) otherwise
     in the best interests of the Company and its stockholders."

          3.  Section 3.1 of the Rights Agreement is hereby amended and restated
in its entirety as follows:

          "3.1 Rights Evidenced by Share Certificates. Until the earlier of (i)
               --------------------------------------
     the tenth day after the Shares Acquisition Date or (ii) the tenth day after
     the date of the commencement of, or first public announcement of the intent
     of any Person (other than the Company, any Subsidiary of the Company, any
     employee benefit plan of the Company or of any Subsidiary of the Company or
     any entity holding shares of capital stock of the Company for or pursuant
     to the terms of any such plan, in its capacity as an agent or trustee for
     any such plan) to commence, a tender or exchange offer the consummation of
     which would result in any Person becoming the Beneficial Owner of Common
     Shares aggregating 20% or more of the then outstanding Common Shares of the
     Company (the earlier of (i) and (ii) being herein referred to as the
     "Distribution Date," whether or not either such date occurs prior to the
     Record Date), (x) the Rights (unless earlier expired, redeemed or
     terminated) will be evidenced (subject to the provisions of Section 3.2)
                                                                 -----------
     by the certificates for Common Shares registered in the names of the
     holders thereof (which certificates for Common Shares shall also be deemed
     to be Right Certificates) and not by separate certificates, and (y) the
     Rights (and the right to receive certificates therefor) will be
     transferable only in connection with the transfer of the underlying Common
     Shares. The preceding sentence

                                       2
<PAGE>

     notwithstanding, prior to the occurrence of a Distribution Date specified
     as a result of an event described in clause (ii) (or such later
     Distribution Date as the Board of Directors of the Company may select
     pursuant to this sentence), the Board of Directors of the Company may
     postpone, one or more times, the Distribution Date which would occur as a
     result of an event described in clause (ii) beyond the date set forth in
     such clause (ii). Nothing herein shall permit such a postponement of a
     Distribution Date after a Person becomes an Acquiring Person, except as a
     result of the operation of the third sentence of Section 1.1. As soon as
                                                      -----------
     practicable after the Distribution Date, the Rights Agent will send, by
     first-class, postage-prepaid mail, to each record holder of Common Shares
     as of the close of business on the Distribution Date, at the address of
     such holder shown on the records of the Company, one or more certificates
     for Rights, in substantially the form of Exhibit B hereto (a "Right
     Certificate"), evidencing one Right (subject to adjustment as provided
     herein) for each Common Share so held. As of the Distribution Date, the
     Rights will be evidenced solely by such Right Certificates."

          4.   The second paragraph of Exhibit C to the Rights Agreement
(SUMMARY OF RIGHTS TO PURCHASE PREFERRED SHARES), is hereby amended and restated
in its entirety as follows:

          "Until the earlier to occur of (i) ten (10) days following a public
     announcement that a person or group of affiliated or associated persons (an
     "Acquiring Person") has acquired, or obtained the right to acquire,
     beneficial ownership of 20% or more of the Common Shares or (ii) ten (10)
     days, or such later date as may be determined by the Board of Directors
     prior to such time as any person or group of affiliated persons becomes an
     Acquiring Person, following the commencement or announcement of an
     intention to make a tender offer or exchange offer the consummation of
     which would result in the beneficial ownership by a person or group of 20%
     or more of the Common Shares (the earlier of (i) and (ii) being called the
     "Distribution Date," whether or not either such date occurs prior to the
     Record Date), the Rights will be evidenced, with respect to any of the
     Common Share certificates outstanding as of the Record Date, by such Common
     Share certificate together with a copy of this Summary of Rights."

          5.   The seventh paragraph of Exhibit C to the Rights Agreement
(SUMMARY OF RIGHTS TO PURCHASE PREFERRED SHARES), is hereby amended and restated
in its entirety as follows:

          "In the event that a Person becomes an Acquiring Person (except
     pursuant to certain cash offers for all outstanding Common Shares approved
     by the Board) or if the Company were the surviving corporation in a merger
     with an Acquiring Person or any affiliate or associate of an Acquiring
     Person and the Common Shares were not changed or exchanged, each holder of
     a Right, other than Rights

                                       3
<PAGE>

     that are or were acquired or beneficially owned by the 20% stockholder
     (which Rights will thereafter be void), will thereafter have the right to
     receive upon exercise that number of Common Shares having a market value of
     two times the then current Purchase Price of the Right. With certain
     exceptions, in the event that the Company were acquired in a merger or
     other business combination transaction or more than 50% of its assets or
     earning power were sold, proper provision shall be made so that each holder
     of a Right shall thereafter have the right to receive, upon the exercise
     thereof at the then current Purchase Price of the Right, that number of
     shares of common stock of the acquiring company which at the time of such
     transaction would have a market value of two times the then current
     Purchase Price of the Right."

          6.   This Second Amendment shall be effective as of the date hereof
and, except as expressly set forth herein, the Rights Agreement shall remain in
full force and effect and be otherwise unaffected hereby.

          7.   This Second Amendment may be executed in any number of
counterparts, each of which, when executed, shall be deemed to be an original
and all such counterparts shall together constitute one and the same document.

                                       4
<PAGE>

          IN WITNESS WHEREOF, the parties have executed this Second Amendment as
of the date first written above.


                                   RESMED INC.



                                   By: /s/ Peter C. Farrell
                                       ---------------------------------
                                       Peter C. Farrell
                                       President


                                   AMERICAN STOCK TRANSFER & TRUST COMPANY

                                   By: /s/ Paula Caroppoli
                                       ---------------------------------
                                       Paula Caroppoli
                                       Vice President

                                       5