Analytical calculation is presented of the QCD radiative corrections
to the rate of the process $b\to c\tau\bar\nu_\tau$
and to the $\tau$ lepton longitudinal polarization
in $\tau\bar\nu_\tau$ rest frame. The results are given
in the form of one dimensional infrared finite integrals
over the invariant mass of the leptons. We argue that this form
may be optimal for phenomelogical applications due to a possible
breakdown of semilocal hadron-parton duality in decays of heavy
flavours.