of neutrinos. Neglecting such terms by imposing the $Z_2$ symmetry, all Higgs boson masses in this model are described in terms of the VEV, the mixing angles and the dimension-less coupling constants $\lambda_i$ in the Higgs potential. This situation is somewhat similar to the two-Higgs-doublet model with the discrete $Z_2$ symmetry [@Glashow:1976nt], in which perturbative unitarity gives upper bounds on all the Higgs boson masses [@Kanemura:1993hm].

In our analysis, all possible two-body elastic scattering channels (91-channels) are taken into account to evaluate the S-wave amplitude matrix in the GM model. Constraints on the Higgs parameters are obtained by imposing the condition of partial wave unitarity on the eigenmatrix of the S-wave amplitude. Masses of all scalar bosons turn out to be bounded from above, some of which receive much stronger bounds as compared to that in the SM (712 GeV). In particular, the mass of at least one of the charged Higgs bosons should be less than about 400 GeV. At least one of the neutral Higgs boson is lighter than 322 GeV. Furthermore, the upper bound of the lightest scalar boson, whatever it would be, can be about 269 GeV. We also find that by using the experimental constraints 