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Complete QCD Corrections to Hadronic $Z$--Decays in Order $α_s^4$

Corrections of order $α_s^4$ for the axial singlet contributions for the decay rates of the $Z$-boson into hadrons are evaluated in the limit of the heavy top quark mass. Combined with recently finished ${\cal O}(α_s^4)$ calculations of the non-signlet corrections, the new results directly lead us to the first {\em complete} ${\cal O}(α_s^4)$ prediction for the total hadronic decay rate of the Z-boson. The new ${\cal O}(α_s^4)$ term in Z-decay rate lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainty in the strong coupling constant $α_s$, as extracted from these measurements, and to a small shift of the central value.