  We demonstrate that almost degenerate Dirac neutrinos of mass of few eV and
transition magnetic moment of the order of ${10}^{-11}$ $\mu_B$ can be obtained
in an ${SU(2)}_L\times {U(1)}_Y$ model with $S_3\times Z_3\times Z_4$ discrete
symmetry and appropriate Higgs fields. Transition magnetic moment of the Dirac
neutrino arises from to the contribution of leptons and charged Higgs fields at
the one loop level.
