  It is shown that the Self-Consistent RPA (SCRPA) approach allows in a very
natural way to restore symmetries, spontaneously broken on the mean field
level. This is achieved via the introduction of a second Lagrange multiplier
which constrains the variance of the symmetry operator to zero. This important
feature of SCRPA, here pointed out for the first time, is illustrated employing
a simplified model of the nuclear superfluidity.
