  We study the $\mu$ problem and the radiative electroweak symmetry breaking in
an extended gauge mediation supersymmetry breaking (GMSB) model, in which the
messenger fields are assumed to couple to the different singlet fields due to
the discrete symmetry. Since the spectrum of superpartners is modified, the
constraint from the $\mu$ problem can be relaxed in comparison with the
ordinary GMSB at least from the viewpoint of radiative symmetry breaking. We
study the consistency of the values of $\mu$ and $B_\mu$ with the radiative
electroweak symmetry breaking and also the mass spectrum of superpartners. We
present such a concrete example in a supersymmetric SU(5) unified model which
is constructed from a direct product gauge structure by imposing the
doublet-triplet splitting.
