We construct a mass matrix for the four neutrino flavors, three active and
one sterile, needed to fit oscillations in all three neutrino experiments:
atmospheric, solar, and LSND, simultaneously. It organizes the neutrinos in
to two doublets whose central values are about 1 eV apart, and whose splitt
ings are of the order of 10(-3) eV. Atmospheric neutrino oscillations are d
escribed as maximal mixing within the upper doublet, and solar as the same
within the lower doubler. Then LSND is a weak transition from one doublet t
o the other. We comment on the Majorana versus Dirac nature of the active n
eutrinos and show that our mass matrix can he derived from an S-2 x S-2 per
mutation symmetry plus an equal splitting rule.