The conventional definition of the running coupling $\alpha_{$\bar 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 $\alpha_{$\bar 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 $\alpha_{$\bar 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 $\overline {MS}$ 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.