  We demonstrate that the solar and atmospheric neutrino data as well as the
recent result of the LSND experiment cannot be satisfied simultaneously with
three light neutrinos if we consider the mass degeneracy for two neutrinos in
the context of an extended Harvard Model based on the gauge group
$SU(2)_{qL}\times {SU(2)}_{lL}\times {U(1)}_Y$ with $S_3\times Z_4$ discrete
symmetry. Assuming two different representation contents under $S_3\times Z_4$
symmetry for pairwise neutrinos and the lone neutrino the present model admits
neutrino masses of the order of 2.8 eV and can fit either solar and atmospheric
neutrino data or the LSND and solar neutrino data.
