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Concentrating on the impact of the very recent top quark discovery, weperform a combined analysis of two strongest constraints on the 2 Higgs doubletmodel, one coming from the recent measurement by CLEO on the inclusivebranching ratio of b->s \gamma decay and the other from the recent LEP data onZ->b b-bar decay. We have included the model predictions for one-loop vertexcorrections to Z->b b-bar through $\epsilon_b$. We find that the $\epsilon_b$constraint excludes most of the less appealing window $\tan\beta\lsim 1$ at 95%C.L. for the measured top mass from CDF, mt=176+/- 8+/-10 GeV. Moreover, itexcludes $\tan\beta\lsim 2$ at 95% C.L. for mt>176 GeV. Combining with the b->s\gamma constraint, only very heavy charged Higgs (>670 GeV) is allowed by themeasured mt from CDF.Comment: To appear in Mod. Phys. Lett. A, 10 Pages(LaTeX)+1 Figure (not  included). The PS figure is available upon request from the author as a file  or a hard cop

IMPLICATIONS OF THE RECENT TOP QUARK DISCOVERY ON TWO-HIGGS DOUBLET MODEL