  Motivated by existing and recent data on possible neutrino oscillations, we
propose a model of four light neutrinos ($\nu_e, \nu_\mu, \nu_\tau$, and a
singlet $\nu_S$) with a pattern of masses and mixing derivable from a $Z_5$
discrete symmetry and the seesaw mechanism. Atmospheric neutrino oscillations
occur between $\nu_\mu$ and $\nu_\tau$ as pseudo-Dirac partners; whereas solar
neutrino oscillations occur between $\nu_e$ and $\nu_S$, a linear combination
of which is massless. Additional oscillations may occur between $\nu_e$ and
$\nu_\mu$ to account for the recent observation of the LSND (Liquid
Scintillator Neutrino Detector) experiment.
