  We study Sogami's generalized covariant derivative method for a $SU(2)_{L}
\times SU(2)_{R} \times U(1)_{B-L} \times SU(3)_{c}$ model that contains
bi-doublet and triplet Higgs bosons. In particular, a detailed study is made on
the minimization conditions of the Higgs potential. It is known that a
minimization condition and certain phenomenology for a extra gauge boson mass
derive a restriction on potential parameters, which requires fine-tuning. We
show that the restriction can be reduced to a condition of Yukawa coupling
constants giving a heavy mass of the right-handed tau neutrino in our model. We
also discuss the consistency among parameter restrictions of our model by
taking phenomenology of the Higgs boson masses into account.
