ARCH FUND INC
497J, 1996-01-10
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<PAGE>
 
January 10, 1996





Securities and Exchange Commission                                VIA EDGAR
Judiciary Plaza
450 Fifth Street, N.W.
Washington, D.C. 20549


Re:    The Arch Fund, Inc. (the "Fund"); File Nos. 2-79285 and 811-3567


Ladies and Gentlemen:

This letter is being transmitted by means of electronic submission by the
Fund pursuant to Rule 497(j) under the Securities Act of 1933, as amended,
and Regulation S-T.

As the assistant secretary of the Fund, I hereby certify that the definitive
Prospectus for the Fund's Short-Intermediate Municipal Portfolio (Trust
Shares) and the Fund's Statement of Additional Information, each dated June 28, 
1995 (as revised January 2, 1996), each of which has been in use since January
2, 1996, which would have been filed by the Fund pursuant to Rule 497(c) do
not differ from those contained in the Funds' most recent registration
statement on Form N-1A, filed pursuant to EDGAR on January 2, 1996.

If you have any questions concerning this filing, please do not hesitate
to call me at (614) 470-8074.

Sincerely,

/s/ Walter B. Grimm

Walter B. Grimm
Assistant Secretary



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