  A simple extension of the standard model is to introduce $n$ heavy
right-handed Majorana neutrinos and preserve its $\rm SU(2)^{}_L \times
U(1)^{}_Y$ gauge symmetry. Diagonalizing the $(3+n) \times (3+n)$ neutrino mass
matrix, we obtain an exact analytical expression for the effective mass matrix
of $\nu^{}_e$, $\nu^{}_\mu$ and $\nu^{}_\tau$. It turns out that the $3\times
3$ neutrino mixing matrix $V$, which appears in the leptonic charged-current
weak interactions, must not be exactly unitary. The unitarity violation of $V$
is negligibly tiny, however, if the canonical seesaw mechanism works to
reproduce the correct mass scale of light Majorana neutrinos. A similar
conclusion can be drawn in the realistic Type-II seesaw models.
