  We analyzed the S_3 invariant Higgs potential with S_3 singlet and doublet
Higgs. We obtained a relation (|v_1|/|v_2|)^2=-sin2phi_2/sin2phi_1 from this
S_3 invariant Higgs potential, where v_1, v_2 and phi_1, phi_2 are vacuum
pectation values and phases of S_3 doublet Higgs, respectively. This relation
could be satisfied exactly by the results |v_1|/ |v_2|=0.207, phi_1=-74.9deg
and phi_2=0.74deg obtained from the previous our work analyzing the
quark/lepton mass and mixing in S_3 invariant Yukawa interaction. Furthermore,
the relation v_S ~ v_D=sqrt{|v_1|^2+|v_2|^2}=174GeV is obtained and then the
coupling strength of Higgs to top quark g_{H_Stt}=m_t/v_S is altered as by a
factor sqrt{2} from the standard value. Introduced the S_3 doublet Higgs, FCNC
are produced in tree level. Predicted branching ratios for rare decays mu^- to
e^-e^+e^-, K^0_L to mu^+\mu^- etc., induced by the FCNC are sufficiently below
the present experimental upper bounds.
