The central bank said it sold $37.6 million at a cut-off price of 7.1401 pounds per dollar, unchanged from its last sale on Monday.
The bank's rates have stayed within a very tight range since the beginning of June, after the bank allowed the pound to weaken in May. It offered $40 million on Wednesday.
On the black market, the dollar changed hands for 7.37 pounds, fractionally weaker than Tuesday's price of 7.36 pounds.
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.