  It is shown, contrary to common belief, that the Fritzsch ansatz for the
quark mass matrices admits a heavy top quark. With the ansatz prescribed at the
supersymmetric grand unified (GUT) scale, one finds that the top quark may be
as heavy as 145 GeV, provided that tan$\beta$ (the ratio of the vacuum
expectation values of the two higgs doublets) $\gg 1$. Within a
non-supersymmetric GUT framework with two (one) light higgs doublets, the
corresponding approximate upper bound on the top mass is $120~ (90)$ GeV. Our
results are based on a general one--loop renormalization group analysis of the
quark masses and mixing angles and are readily applied to alternative mass
matrix ans\"{a}tze.
