The central bank has held the official exchange rate unchanged for four months since letting the pound weaken at the beginning of 2015. This weakening and other measures have helped reduce black market trading.
In Sunday's auction the bank said it had offered $40 million and sold $37.8 million at a cut-off price of 7.5301 pounds per dollar, unchanged from Thursday's rate.
On the black market the pound was trading at 7.68 pounds to the dollar on Sunday, a trader said, slightly weaker than Thursday's rate of 7.65.
Black market traders say volumes have fallen sharply since the central bank's drive to stamp out their transactions, which has included since February a cap on the amount of dollars that can be deposited in banks.