  The self-consistent random-phase approximation (SCRPA) is reexamined within a
multilevel-pairing model with double degeneracy. It is shown that the
expressions for occupation numbers used in the original version of SCRPA
violate the particle number for non-symmetric particle-hole ($ph$) spectra. A
renormalization is introduced to restore the particle number, which leads to
the expressions of occupation numbers similar to those derived by Hara et al.
for the ph case. The results of calculations within the $ph$-symmetric case
show that this number-conserving SCRPA yields the energies of the ground state
and first excited state of the system with $\Omega+2$ particles relative to the
ground state of the system with $\Omega$ particles in close agreement with
those obtained within the original SCRPA. However it gives a slightly larger
correlation energy.
