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.

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