  we explore the consequences of assuming a simple 3-parameter form, first
without T-violation, for the neutrino mass matrix M in the basis $\nu_e,
\nu_\mu, \nu_\tau$ with a new symmetry. This matrix determines the three
neutrino masses m_1, m_2, m_3, as well as the mapping matrix U that
diagonalizes M. Since U, without T-violation, yields three measurable
parameters $s_{12}, s_{23}, s_{13}$, our form expresses six measurable
quantities in terms of three parameters, with results in agreement with the
experimental data. More precise measurements can give stringent tests of the
model as well as determining the values of its three parameters. An extension
incorporating T-violation is also discussed.
