  Recently, many authors showed that if the solar and atmospheric neutrino data
are both described by maximal mixing vacuum oscillations at the relevant mass
scale, then there exists a unique bi-maximal lepton mixing matrix for three
neutrino flavors. We construct the lepton mass matrices from the symmetry
principle so that maximal mixings for the atmospheric and the solar neutrino
vacuum oscillations are naturally generated. Although the hierarchical patterns
of the lepton sector are quite different from each other, we show how two
different mass matrices suggested in this work can be generated in a unified
way. We also give comments on possible future tests of the bi-maximal lepton
mixing matrix.
