  We analyze finite supersymmetric SU(5) GUT taking into account the problem in
the Higgs potential and threshold corrections to gauge and Yukawa couplings at
GUT and SUSY scales which is important in case of large $\tan \beta$ model. We
find that even with these finiteness conditions, which are very restrictive,
there are parameter regions where low-energy experimental values are
consistently reproduced and the Higgs potential actually realizes both
constraints for large $\tan \beta$ and radiative electroweak symmetry breaking,
provided that a free parameter is introduced in the boundary condition of the
Higgs mixing mass parameter.
