  A four-parameter Majorana neutrino mass matrix is proposed, which is exactly
diagonalizable with two mixing angles, one of which is pi/4 and the other large
but less than pi/4. The form of this mass matrix allows seven realizations of
the present data on atmospheric and solar neutrino oscillations: three have the
normal hierarchy, two have the inverse hierarchy, and two have three nearly
degenerate masses. The possible inclusion of CP violation is also discussed.
