the model is allowed to have the mass terms for the neutrinos by assigning of lepton number $-2$ to the complex triplet field, i(h\_)\_[ab]{}\_[La]{}\^TC\_2\_[Lb]{}+[h.c.]{}, where $\hat \chi=\frac{\tau^i}{2}(P^\dag\chi)^i$. In order to generate the tiny neutrino masses the Yukawa coupling $h_\nu$ should be fine-tuned to be very small as $h_\nu\sim {\cal O}(10^{-12})$ for the triplet VEV of order 100 GeV. Since we would like to avoid such fine tuning with respect to the neutrino masses, we require the discrete $Z_2$ symmetry in the Higgs potential and prohibit the last two terms in Eq.(\[potential\])[^3]. Therefore, quarks and leptons couple to the $SU(2)_L$ doublet field $\Phi$ in the same way as the SM Yukawa coupling, but do not to the triplet $\Delta$ at the tree level. Because all the masses of quarks and leptons are obtained from the VEV in $\Phi$, we do not have to worry about FCNC, and it is expected to appear at most at the same level as that in the SM. This property of the coupling to fermions would give an additional constraint on the value of the doublet-triplet mixing angle $\theta_H^{}$ by $\tan\theta_H^{}< {\cal O}(1)$, since large values of $\tan\theta_H^{}$ $(\gg 1)$ imply that the top-Yukawa coupling is 