  The Friedberg-Lee (FL) symmetry is generated by a transformation of a
fermionic field $q$ to $q + \xi z$. This symmetry puts very restrictive
constraints on allowed terms in a Lagrangian. Applying this symmetry to $N$
fermionic fields, we find that the number of independent fields is reduced to
$N-1$ if the fields have gauge interaction or the transformation is a local
one. Using this property, we find that a seesaw model originally with three
generations of left- and right-handed neutrinos, with the left-handed neutrinos
unaffected but the right-handed neutrinos transformed under the local FL
translation, is reduced to an effective theory of minimal seesaw which has only
two right-handed neutrinos. The symmetry predicts that one of the light
neutrino masses must be zero.
