  We show that Yukawa couplings of bottom quarks and tau leptons can be unified
in a non-supersymmetric SU(5) model. We introduce an arbitrary number of
right-handed neutrinos. Their masses and Yukawa couplings that satisfy the
unification condition by renormalization group evolution are shown. In the case
that the grand unification scale is $10^{15.5}$GeV and three right-handed
neutrinos have the same mass, the upper bound on their mass is $\sim
10^{14.1}$GeV.
