Exhibit 99.1

Permian Basin Royalty Trust

News Release

PERMIAN BASIN ROYALTY TRUST
ANNOUNCES SEPTEMBER CASH DISTRIBUTION

     DALLAS, Texas, September 20, 2004 — Bank of America, N.A., as Trustee of the Permian Basin Royalty Trust (NYSE — PBT), today declared a cash distribution to the holders of its units of beneficial interest of $.097042 per unit, payable on October 15, 2004, to unit holders of record on September 30, 2004.

     This month’s distribution increased from the previous month due primarily to higher oil and gas prices, as well as slightly higher oil and gas production in the Waddell Ranch properties. Production for Waddell Ranch and the Texas Royalty Properties combined for oil and gas respectively was 74,319 bbls and 322,432 mcf. The average price for oil was $37.67 per bbl and for gas was $6.10 per mcf. This would primarily reflect production for the month of July. Capital expenditures were approximately $432,988. The numbers provided reflect what was net to the Trust.

     For information, including the latest financial reports on Permian Basin Royalty Trust, please visit our website at
http://www.pbt-permianbasintrust.com/.

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Contact: Ron E. Hooper
Senior Vice President
Bank of America, N.A.
Toll Free — 877.228.5085