CAIRO, Sept 3 (Reuters) - Egypt's pound held steady at a central bank dollar sale on Wednesday, with the bank saying it sold $37.6 million at a cut-off price of 7.1401 pounds per dollar, unchanged from Monday's rate.

In the unofficial market, the pound was also steady, trading at 7.38 to the dollar, one trader 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 Wednesday.

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 Lin Noueihed, editing by John Stonestreet)