Long Island's North Fork Bancorp. finally has found an opening into the coveted New England market.

The $6.6 billion-asset company, based in Mattituck, N.Y., agreed last week to buy Branford Savings Bank in southeastern Connecticut for $38 million in stock. Branford Savings operates five branches in New Haven County, directly across Long Island Sound from North Fork's branches in Nassau and Suffolk counties, NY.

Branford Savings will become a subsidiary of North Fork, which has been seeking to buy a midsize community bank in Connecticut.

Officials at North Fork, which operates 82 offices in New York, said they plan to use Branford Savings as a highly efficient, aggressive, and low-cost base from which to increase their funding throughout New England to support lending in the New York area.

The company hopes to attract depositors by promoting deposit-by-mail and offering high interest rates.

But North Fork officials said the company would limit lending and other resources to the bank's existing market.

"From Branford, we intend to pursue a vigorous campaign of deposit- gathering throughout New England," said North Fork president and chief executive officer John A. Kanas. "We believe that the model we intend to create will serve as a blueprint for a much larger institution in a short period of time."

North Fork is paying about 2.2 times book value and 16 times earnings for $187 million-asset Branford Savings, a big premium for a bank that three years ago faced possible regulatory takeover as sour loans and heavy losses mounted.

At Dec. 31, 1994, the struggling bank was battling bad loans that totaled about 8.48% of its assets. Its loan-loss reserve covered only 32% of the nonperformers, and the bank suffered a loss of $854,000 that year.

However, in November 1994, it completed a rights offering to shareholders that netted about $11 million.

Since then, Branford Savings has steadily improved, prompting regulators to lift a 1991 cease-and-desist order in October 1995.

On July 29, it reported a $1.1 million profit for the first half of 1997.

It had earned $1.8 million for all of last year.

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