  We present the two-loop master integrals relevant to the ${\mathcal O}(\alpha
\alpha_s)$-corrections to the decay $H \rightarrow b \bar{b}$ through a $H t
\bar{t}$-coupling. We keep the full dependence on the heavy particle masses,
but neglect the $b$-quark mass. The occurring square roots can be rationalised
and the result is expressed in terms of multiple polylogarithms.
