The conventional definition of the running coupling
*alpha*_{MS}(mu) in quantum chromodynamics is based on a
solution to the renormalization group equations which treats quarks as
either completely massless at a renormalization scale *mu* above their
thresholds or infinitely massive at a scale below them. The coupling
is thus nonanalytic at these thresholds. In this paper we present an
analytic extension of *alpha*_{MS}(mu) which incorporates
the finite-mass quark threshold effects into the running of the
coupling. This is achieved by using a commensurate scale relation to
connect *alpha*_{MS}(mu) to the physical
*alpha*_{V} scheme at specific scales, thus naturally
including finite quark masses. The analytic-extension inherits the
exact analyticity of the *alpha*_{V} scheme and matches
the conventional MS scheme far above and below mass
thresholds. Furthermore just as in *alpha*_{V} scheme,
there is no renormalization scale ambiguity, since the position of the
physical mass thresholds is unambiguous.