The central bank said it offered $40 million on Sunday and sold $38.4 million at a cut-off price of 7.5301 pounds per dollar CBEO, unchanged from the last auction on Thursday.
The central bank has now kept the official exchange rate steady for more than a month after letting the pound weaken in an effort to wipe out black market trading.
The pound was broadly steady on the parallel market on Thursday.
One trader said the dollar was selling for 7.67 pounds, just slightly weaker than Thursday's rate of 7.66. Analysts say the central bank may have decided to stabilise the currency to stop it from depreciating too much and because it hopes other recent measures will have an impact.
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.
As well as letting the pound depreciate, the central bank gave banks permission late last month to widen the band around the official rate at which they can trade dollars and imposed a limit on dollar deposits in banks.