New Jersey is awash with discount outlet malls, and William H. Turner likes to shop. But after almost a year of intensive searching, the chairman and chief executive of Chemical New Jersey Holdings has yet to find the bargain he seeks.

Mr. Turner, a senior vice president of Chemical Banking Corp., has a mandate to catapult the nation's third-largest bank from an also-run to a competitor in the Garden State. The New York-based company entered the neighboring state in 1989 by purchasing Horizon Bancorp, but has been stuck with a fifth-place market share ever since.

"We don't have as many branches as we'd like to have," Mr. Turner acknowledged in a recent interview. "The right deal just hasn't come along for us." But Mr. Turner, 53, continues to assert that he wants to double the bank's New Jersey assets of $5.6 billion in three to five years.

The New Jersey native, who started his banking career at Chemical 31 years ago, has done a credible job with profits at the 130-branch New Jersey operation in recent months.

Chemical does not break out its New Jersey results. But the subsidiary earned $71.2 million in 1992, after losing $9.7 million in 1991 and $79.8 million in 1990, according to Ferguson & Co.

With return on average common equity at 22% and return on assets of 1.37$ it is now on of the most. profitable banks' in the state.

But the executive knows that his bosses want more.

John McGillicuddy, Chemical's chairman and chief executive, has said that Chemical should rank among the top three in each of its banking markets.

In New Jersey, Chemical lags behind First Fidelity Bancorp., UJB Financial Corp. Midlantic Corp., and National Westminster Bancorp Inc.

But Mr. Turner also has the confidence of his bosses. He was put in charge of Chemical's branch banking network in 1982, after stints in consumer, corporate, and international banking. Later in the decade, he ran the bank's Middle East and Africa group out of Beirut.

He returned to New Jersey with the Horizon purchase in 1989, but it remains a small part of his empire. Mr. Turner also oversees Chemical's large and highly profitable middle-market business, its New York retail business, and private banking, which includes a trust link in Princeton, N.J.

Mr. Turner, noting that experience has given him the discipline to wait, said he has walked from a few small acquisitions in northern New Jersey that were priced too high. And he adds that he has no regrets about losing some deals. Sources said he was referring to Howard Savings Bank, which was acquired by First Fidelity for $73.5 million.

Mr. Turner declines to talk about specific banks. But year ago an internal memo listed about a dozen New Jersey banks as potential acquisition targets. They ranged in size from the state's largest, such as First Fidelity, to small savings banks.

He said the ultimate decision -- whether to make fill-in acquisitions or join forces with a regional bank to become a northeastern giant well beyond New York City -- has not been made.

"If you're looking predominantly at New Jersey, that would have a lot of appeal because you get the cost savings of overlapping branches," said Mr. Turner.

"On the other hand, you don't want to spend all your efforts on New Jersey if there's something that would give you coverage in a few states."

Meanwhile, Mr. Turner isn't standing still. Chemical has opened 11 branches from scratch since 1989, including one last month in affluent Bergen County. "If the right thing doesn't come along, we're looking at opening three to five de novo branches a year," he says.

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