  We carry out diagonalization of a kind of Majorana neutrino mass matrix
$M=M_\nu M_\nu^\dagger$ of which Real part and Imaginary part are commutative.
For the kind of matrix M, it is shown in a model-independent way that $\delta =
\pm\pi/2$ which implies the maximal strength of CP violation in neutrino
oscillations and atmospherical mixing angle would be in the ranges, $\pi/4 <
\theta_{23} < 3\pi/4$, or $-3\pi/4<\theta_{23} < - \pi/4$. It is shown that the
kind of Hermitian Majorana neutrino mass matrix M has only five real parameters
and furthermore, only one free real parameter (A or D) if using the measured
values of three mixing angles and mass squared differences as inputs.
