  We apply the sum-over-states approach to calculate partial contributions to
the parity non-conservation (PNC) in cesium [Porsev {\em et al}, Phys. Rev. D
{\bf 82}, 036008 (2010)]. We have found significant corrections to two
non-dominating terms coming from the contribution of the core and highly
excited states ($n>9$, the so called {\em tail}). When these differences are
taken into account the result of Porsev {\em et al}, $E_{\rm PNC} =
0.8906\,(24) \times 10^{-11}i(-Q_W/N)$ changes to $0.8977\,(40)$, coming into
good agreement with our previous calculations, $0.8980\,(45)$. The
interpretation of the PNC measurements in cesium still indicates reasonable
agreement with the standard model ($1.5\,\sigma$), however gives new
constraints on physics beyond it.
