  We improve the calculation of the supersymmetric $O(\alpha_s)$ QCD
corrections to the decays of Higgs bosons into quarks and squarks in the
Minimal Supersymmetric Standard Model. In the on-shell renormalization scheme
these corrections can be very large, which makes the perturbative expansion
unreliable. This is especially serious for decays into bottom quarks and
squarks for large $\tan\beta$. Their corrected widths can even become negative.
We show that this problem can be solved by a careful choice of the tree-level
Higgs boson couplings to quarks and squarks, in terms of the QCD and SUSY QCD
running quark masses, running trilinear couplings $A_q$, and on-shell
left-right mixing angles of squarks. We also present numerical results for the
corrected partial decay widths for the large $\tan\beta$ case.
