CAIRO, July 31 (Reuters) - The Egyptian pound was stable at a central bank dollar sale on Thursday and weakened slightly on the black market.

The central bank said it sold $37.6 million at a cut-off price of 7.1401 pounds per dollar, unchanged from its most recent sale last Thursday, before the Muslim Eid holiday.

The rate for the dollar sales has stayed within a very tight range since the beginning of June, after the bank allowed the pound to weaken in May. It had offered $40 million on Thursday.

On the black market, the dollar changed hands for 7.40 pounds, one trader said, weaker than the rate of 7.39 pounds a week earlier.

The rates at which banks are allowed to trade dollars are determined by the results of the central bank sales, giving the bank effective control over official exchange rates. (Reporting By Stephen Kali; Editing by Susan Fenton)