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.
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