  In this paper we obtain the exact mass-eigenstates of the Majorana physical
neutrinos. We start by taking into account a general $3\times3$ mass matrix
without any CP-phase violation. It is then diagonalized by exactly solving an
appropriate set of equations. The solution supplies straightforwardly the mass
eigenvalues depending on the diagonal entries and mixing angles. Finally, the
consequences of these analytical expressions are discussed assuming various
phenomenological restrictions such as conserving the global lepton number
$L=L_{e}-L_{\mu}-L_{\tau}$ and the $\mu-\tau$ interchange symmetry. The minimal
absolute mass in the neutrino sector is also obtained since the two plausible
scenarios invoked above are employed.
