The largest block of stock ever traded on the New York Stock Exchange changed hands yesterday, 6.3 million shares of Federal National Mortgage Corp. of Washington.

In dollar value, it was the sixth-largest transaction, worth $77 million.

The previous record belonged to U.S. Steel Corp. for a 5.2-million-share block sold June 16 of this year. The most expensive single transaction to cross the tape was a $103 million block of 1.2 million shares of Cutler-Hammer back in 1978.

The record trade was arranged by Fannie Mae through the firm of Goldman, Sachs & Co. In the debt-equity swap, Fannie Mae, a government-chartered corporation that makes a secondary market in government-backed mortgages, retired some of its old bonds and issued new stock. The shares were sold at 12 1/4 to individual investors by Goldman, Sachs.

Thanks to the transaction, troubled Fannie Mae stands to make a one-time profit of $28 million in its third quarter. The corporation suffered a loss of $43.1 million in the second quarter. The proceeds from the sale of stock will enable Fannie Mae to buy about $2.5 billion in mortgages from savings and loan associations, banks and other lenders, in turn making more funds available for additional mortgage loans.