  We present in analytic form the matching conditions for the strong-coupling
constant alpha_s^(n_f)(mu) at the flavor thresholds to four loops in the
modified minimal-subtraction scheme. Taking into account the present knowledge
on the coefficient beta_4 of the Callan-Symanzik beta function of quantum
chromo-dynamics, we thus derive a five-loop formula for alpha_s^(n_f)(mu)
together with appropriate relationships between the asymptotic scale parameters
Lambda^(n_f) for different numbers of flavors n_f.
