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An analysis is given of the $b\ensuremath{-}\ensuremath{\tau}$ Yukawa coupling unification in view of the recent result from Brookhaven on ${g}_{\ensuremath{\mu}}\ensuremath{-}2$ and under the constraint of $\stackrel{\ensuremath{\rightarrow}}{b}s+\ensuremath{\gamma}.$ We explore $b\ensuremath{-}\ensuremath{\tau}$ unification under the above constraints for nonuniversal boundary conditions for soft supersymmetry breaking parameters. We find new regions of the parameter …