  A new version of random phase approximation is proposed for low-energy
harmonic vibrations in nuclei. The theory is not based on the quasi-particle
vacuum of the BCS/HFB ground state, but on the pair condensate determined in
Ref. [4]. The current treatment conserves the exact particle number all the
time. As a first test the theory is considered in two special cases: the
degenerate model (large pairing limit) and the vanished-pairing limit.
