When relating the strong coupling $\alpha_s$, measured at the scale of the
$Z$ boson mass, to its numerical value at some higher energy, for example
the scale of Grand Unification, it is important to include higher order
corrections both in the running of $\alpha_s$ and the decoupling of the
heavy particles. We compute the two-loop matching coefficients for
$\alpha_s$ within the Minimal Supersymmetric Standard Model (MSSM) which are
necessary for a consistent three-loop evolution of the strong coupling
constant. Different scenarios for the hierarchy of the supersymmetric scales
are considered and the numerical effects are discussed. We find that the
three-loop effects can be as large as and sometimes even larger than the
uncertainty induced by the current experimental accuracy of $\alpha_s(M_Z)$.
