  A model with flavor-triplet Higgs scalars \phi_i (i=1,2,3)is investigated
under a permutation symmetry S_3 and its symmetry breaking. A possible S_3
breaking form of the Higgs potential whose vacuum expectation values v_i=<
\phi_i> satisfy a relation v_1^2 +v_2^2 +v_3^2 ={2/3}(v_1 +v_2 +v_3)^2 is
investigated, because if we suppose a seesaw-like mass matrix model M_e = m
M^{-1} m with m_{ij} \propto \delta_{ij} v_i and M_{ij} \propto \delta_{ij},
such a model can lead to the well-known charged lepton mass relation m_e +m_\mu
+m_\tau = {2/3} (\sqrt{m_e}+\sqrt{m_\mu} +\sqrt{m_\tau})^2.
