The bank offered $40 million at the sale and said it had sold $38.4 million at a cut-off price of 7.1401 pounds to the dollar, a rate unchanged from its last sale 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.
In the unofficial market, one money changer said the pound was trading at 7.75 to the dollar on Thursday, stronger than levels around 7.84 quoted on Wednesday.
The central bank introduced a fourth weekly dollar auction in December as part of efforts to curb a flourishing currency black market after the gap between the official and unofficial rates widened.
The move has so far failed to narrow the gap substantially.