CAIRO, Sept 1 (Reuters) - Egypt's pound held steady at a central bank dollar sale on Monday, with the bank saying it sold $37.6 million at a cut-off price of 7.1401 pounds per dollar, unchanged from last week's rate.

In the unofficial market, the pound was steady, trading at 7.38 to the dollar, traders said.

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

The rates at which banks are allowed to trade dollars are determined by the results of central bank sales, giving the bank effective control over official exchange rates. (Reporting by Michael Georgy; Editing by Toby Chopra)