The central bank has held the official exchange rate steady 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 and sold $40 million at a cut-off price of 7.5301 pounds per dollar , unchanged from Thursday's rate.
The pound was trading at 7.67 pounds to the dollar, one trader said, slightly stronger from Thursday's rate.
Another trader said it was also trading at 7.68 pounds like Thursday.
Auctions take place on Sunday, Tuesday and Thursday every week.
Black market traders say volumes have fallen sharply since the central bank's drive to stamp out their transactions, which, since February, has included a cap on the amount of dollars that can be deposited in banks.