  In the $SU(6) \times SU(2)_R$ string-inspired model, we evolve the couplings
and the masses down from the string scale $M_S$ using the renormalization group
equations and minimize the effective potential. This model has the flavor
symmetry including the binary dihedral group $\tilde{D}_4$. We show that the
scalar mass squared of the gauge non-singlet matter field possibly goes
negative slightly below the string scale. As a consequence, the precocious
radiative breaking of the gauge symmetry down to the standard model gauge group
can occur. In the present model, the large Yukawa coupling which plays an
important role in the symmetry breaking is identical with the colored Higgs
coupling related to the longevity of the proton.
