  We study the muon magnetic dipole moment and the Higgs mass in the framework
of the supersymmetric SU(5) models. In this analysis, all the relevant
parameters in the Lagrangian are taken to be free; in particular, assumption of
the universal scalar mass is not adopted. Negative search for the Higgs boson
at the LEP II experiment sets an important constraint on the supersymmetric
contribution to the muon magnetic dipole moment a_\mu(SUSY). It is shown that,
for a fixed value of the lightest Higgs mass, the maximum possible value of
a_\mu(SUSY) becomes significantly larger in the general SU(5) case compared to
the case of the universal scalar mass (i.e., the case of the so-called
``CMSSM''). We also point out that, if we take relatively large value of the
trilinear scalar couplings, the constraint from the Higgs mass is drastically
relaxed. In this case, a_\mu(SUSY) can be as large as \sim 50\times 10^{-10}
even for small value of \tan\beta (say, for \tan\beta=5).
