  The use of MS-like renormalization schemes in QCD requires an implementation
of nontrivial matching conditions across thresholds, a fact often overlooked in
the literature. We shortly review the use of these matching conditions in QCD
and check explicitly that the prediction for $\alpha_s(M_Z)$, obtained by
running the strong coupling constant from the $M_\tau$ scale, does not
substantially depend on the exact value of the matching point chosen in
crossing the $b$-quark threshold when the appropriate matching conditions are
taken into account.
