  The renormalized mass of the bottom quark is calculated at the two loop level
to order ${\cal O}(\alpha_s G_F M_t^2)$ in the $\msbar$ renormalization scheme.
Different strategies for the computation are outlined. The result is applied to
the partial decay rate $\Gamma(H\rightarrow b\bar{b})$ of the Higgs boson into
bottom quarks. Expressing the width in terms of the running mass instead of the
bottom pole mass allows to treat the ${\cal O}(\alpha_s G_F M_t^2)$ radiative
corrections on the same footing as is commonly used in pure QCD calculations.
The numerical values for the corrections are given and the sizes of different
contributions are compared.
