  The ansatz that the right-handed neutrino fields are real spinors is proposed
in this letter. We naturally explain why the right-handed neutrinos don't feel
the electroweak interactions and why there is neutrino mixing. It is found that
the Majorana representation of Dirac equation is uniquely permitted in our
scenario. With this ansatz, we predict that: 1. there are at least four species
of neutrinos; 2. the mass matrix of neutrinos must be traceless; 3. there is CP
violation in the lepton sector. The difference between our scenario and the Zee
model is discussed also.
