Egypt, which depends heavily on imports, is facing a foreign currency crisis and is under increasing pressure to devalue the pound, but the bank surprised markets when it strengthened the pound by 20 piasters in November and held it steady ever since.
The central bank sold $38.8 million at a cut-off price of 7.7301 pounds to the dollar on Tuesday, unchanged from the previous auction.
The official rate is still far stronger than the black market rate, which was weakened to 9.12 pounds per dollar on Tuesday, weaker than the 9.10 pounds quoted black market traders on Sunday.
Trading for dollars in the black market is now limited to regular customers, traders said, as they feared a government crackdown. Last week the central bank shut down four exchange bureaus for trading with unofficial rates.
Egypt has been starved of foreign currency since an uprising in 2011 ousted autocrat Hosni Mubarak but drove away tourists and foreign investors - major sources of hard currency.
Its foreign currency reserves have tumbled from $36 billion in 2011 to $16.48 billion at the end of January, and the country has been rationing dollars through the weekly dollar auctions to banks, keeping the pound artificially strong.
The central bank has repeatedly said it is not planning a devaluation but economists, business people and money changers all say it cannot hold out forever.
Egypt is reluctant to devalue the currency due to concerns that this would fuel inflation, already in double digits.
The bank's Monetary Policy Committee raised benchmark rates by 50 basis points last month, citing inflationary pressures.