  Recent interest in horizontal symmetry model building has been driven mainly
by the large top mass and hence strong hierarchy in quark masses, and the
possibility of appropriately constrained soft squark mass matrices, in place of
an assumed universality condition, for satisfying the relevant FCNC
constraints. Here we present the first successful SUSY-$SU(5)$ model that has
such a feature. The horizontal symmetry is a gauged $(Q_{12} \times U(1))_H$
($\subset (SU(2) \times U(1))_H$). All nonrenormalizable terms compatible with
the symmetry are allowed in the mass matrix constructions. Charged lepton
masses can also be accommodated.
