  The mass matrix of three Majorana neutrinos of equal mass is not necessarily
proportional to the identity matrix, but expressible in terms of two angles and
one phase. We discuss how such a mass matrix may be stable or unstable against
radiative corrections. We then propose a model with additional explicit
breaking of the threefold degeneracy to account for the atmospheric neutrino
data, while the radiative breaking explains the solar neutrino data, using the
large-angle Mikheyev-Smirnov-Wolfenstein solution. Our model requires a nonzero
effective $\nu_e$ mass for neutrinoless double beta decay close to the present
experimental upper limit of 0.2 eV.
