  We examine a recently proposed symmetry/condition by Friedberg and Lee in the
framework where three right-handed neutrinos are added to the spectrum of the
three-family Minimal Standard Model. It is found that the right-handed
neutrinos are very special, with respect to this symmetry. In the symmetry
limit the neutrinos are massless and that may be a hint about why they are
light. Imposed as a condition and not as a full symmetry, we find that one of
the three right-handed neutrinos simply decouples (has only gravitational
interactions) and that there is a massless interacting neutrino. The possible
relation of the model to the see-saw mechanism is briefly discussed.
