  Recently, Nishiura and the author have proposed a unified quark-lepton mass
matrix model under a family symmetry U(3)$\times$U(3)$'$. The model can give
excellent parameter-fitting to the observed quark and neutrino data. The model
has a reasonable basis as far as the quark sector, but the form of the
right-handed neutrino mass matrix $M_R$ does not have a theoretical grand, that
is, it was nothing but a phenomenological assumption. In this paper, it is
pointed out that the form of $M_R$ is originated in structure of neutrino mass
matrix for $(\nu_i, N_\alpha)$ where $\nu_i$ ($i=1,2,3$) and $N_\alpha$
($\alpha=1,2,3$) are U(3)-family and U(3)$'$-family triplets, respectively.
