  The quasiparticle time blocking approximation (QTBA) is considered as a model
for the description of excitations in open-shell nuclei. The QTBA is an
extension of the quasiparticle random phase approximation that includes
quasiparticle-phonon coupling. In the present version of the QTBA, the pairing
correlations are included within the framework of the BCS approximation. Thus,
in this model, the $0^+$ spurious states appear, which are caused by the
breaking of the symmetry related to the particle-number conservation. In this
work, the method is described which solves the problem of the $0^+$ spurious
states in the QTBA with the help of the projection technique. The method is
illustrated by calculations of $0^+$ excitations in $^{120}$Sn nucleus.
