NUVEEN UNIT TRUSTS SERIES 40
497, 1999-05-28
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                                                               File No. 811-2271
                                                                     Rule 497(d)



                         Supplement Dated May 28, 1999
                               to the Prospectus

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                          Nuveen Tax-Free Unit Trusts

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     John Nuveen & Co. Incorporated ("Nuveen"), the Sponsor of the Nuveen Tax-
Free Unit Trusts, is modifying the Unit purchase program available to Nuveen
employees and other affiliated persons. Accordingly, notwithstanding anything to
the contrary in the Prospectus:

(1)  The reduced sales charge program described in the Prospectus for officers,
     directors or bona fide, full-time employees of Nuveen, Nuveen Advisory
     Corp., Nuveen Institutional Advisory Corp., Rittenhouse Financial Services,
     Inc. or The John Nuveen Company, including in each case these individuals
     and their immediate family members (as defined in the Prospectus) is no
     longer applicable.

(2)  Units may be purchased in the primary market with sales charges of 1.70% of
     the Public Offering Price for National and State Long Term Trusts, 1.35% of
     the Public Offering Price for Long Intermediate Trusts, 1.20% of the Public
     Offering Price for National and State Intermediate Trusts, and 1.0% of the
     Public Offering Price for Short Term Trusts, by officers, directors and
     bona fide, full-time employees of Nuveen, Nuveen Advisory Corp., Nuveen
     Institutional Advisory Corp., Rittenhouse Financial Services, Inc. and The
     John Nuveen Company, including in each case these individuals and their
     spouses, minor children, and parents. However, purchases by parents must be
     made through a registered broker-dealer.

     Such investors may also purchase Units in the secondary market at the
     Public Offering Price for non-breakpoint purchases minus the concession the
     Sponsor typically allows to brokers and dealers for non-breakpoint
     purchases. Investors who purchase Units as described above will not receive
     sales charge reductions for quantity purchases.

     Dealers are not entitled to receive any dealer concession for any sales
     made to Unitholders receiving the reduced sales charges specified above.



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