The Federal Home Loan Bank Board has taken the unprecedented step of permitting a savings and loan to buy a healthy thrift institution in another state without first buying an ailing S&L there.

The purchaser is Great American First Savings Bank of San Diego, where bank board Chairman Edwin Gray was a top executive until 1983, when he took his present job as chief of the federal agency that regulates the savings and loan industry. The bank board said Gray did not participate in the merger decision because of his earlier affiliation with Great American.

Under the merger plan approved 10 days ago, Great American will purchase Home Federal Savings and Loan Association, a healthy Tuscon thrift with $2.4 billion in assets. In exchange, Great American, which has assets of $8.2 billion, has agreed to buy two troubled California thrifts that have assets of $71.9 million.

Until last week, the bank board had permitted a healthy thrift to cross state lines only if it acquired an ailing institution in the process. The bank board previously had allowed healthy savings associations to buy ailing thrifts in other states and had permitted healthy institutions to merge across state lines if they also bought a failing thrift in the state they wanted to enter.

Perpetual American, the largest thrift in the District, had to buy failing thrifts in Maryland and Virginia in 1982 before it could enter those states, for example.

Similarly, Meritor Financial Group of Philadelphia last year was permitted to buy a healthy S&L in Florida only in exchange for buying an ailing one in the state as well as two troubled institutions in the metropolitan Washington area.

The idea behind such "tit-for-tat" sales is that the bank board dangles the prospect of entering an attractive market as bait to increase the attractiveness of taking on a sick institution.

The bank board said that "there was an absence of FSLIC problem cases in Arizona," however, so it could not require Great American to purchase a troubled thrift in that state before allowing it to buy healthy Home Federal.

A bank board spokesman said the unprecedented action was "not a change in policy" and might or might not occur again, depending on circumstance.

Even though Great American is insured by FSLIC, it is a state-chartered thrift and therefore needs no waiver of federal law or bank board regulation barring federally chartered institutions from crossing state lines without first buying a troubled thrift, a bank board spokesman said.

A spokesman for Great American said the S&L will pay $102 million in cash for the stock of Home Federal, which had record earnings of $16.6 million last year. He said that the merger will make Great American, which earned $45.6 million last year, the 10th-largest S&L in the country, up from the 15th, when measured by asset size.

Although Great American had to buy failing thrifts within the borders of its own home state before it was allowed to enter the lucrative Arizona market, the ability to enter a new state without buying a faltering institution there greatly enhances the value of the new market for a purchaser.

Selling an ailing thrift to a healthy institution is much less costly to the Federal Savings and Loan Insurance Corp., which federally insures each deposit up to $100,000, than closing an institution and selling its assets.

The FSLIC, which is run by the bank board, will pay Great American $1.2 million to take over First Federal Savings and Loan Association, a Reading, Calif., institution with assets of $38.5 million, and Hacienda Federal Savings and Loan Association of Oxnard, Calif., which has assets of $33.4 million.

The two troubled thrifts had a negative net worth of $24 million -- meaning their liabilities exceeded their assets by that amount.