  We consider the case that the solar neutrino deficit is due to the vacuum
oscillation. The lepton mass matrices with nearly bi-maximal mixings are needed
in order to explain both solar and atmospheric neutrino deficit. A texture with
the symmetry of flavour democracy or $S_3$ has been investigated by taking
account of the symmetry breaking terms of the charged lepton mass matrix. It is
found that predicted mixings can be considerably changed from the neutrino
mixings $\sin^2 2\th_\odot\simeq 1$ and
  $\sin^2 2\th_{\rm atm}\simeq 8/9$ at the symmetric limit. The correlation
between $|U_{e3}|$ and $|U_{e1}U_{e2}^*|$ is also presented. The test of the
model is discussed by focusing on the three flavor analyses in the solar
neutrinos, atmospheric neutrinos and long baseline experiments.
