  Future colliders aim to provide highly precise experimental measurements of
the properties of the Higgs boson. In order to benefit from these precision
machines, theoretical errors in the Higgs sector observables have to match at
least the experimental uncertainties. The theoretical uncertainties in the
Higgs sector observables can be reduced by including missing higher-order terms
in their perturbative calculations. In this direction, we compute the mixed
QCD-electroweak corrections at ${\mathcal O}(\alpha \alpha_s)$ to the Higgs
decay into four charged leptons by considering the golden decay channel, $ H
\to e^+e^-\mu^+\mu^-$. Due to color conservation, these corrections receive
contributions only from the two-loop virtual diagrams. In the complex mass
scheme, we find that the mixed QCD-electroweak corrections to the partial decay
width, relative to the leading order predictions, are positive and about
$0.27\%$ for $\alpha_s(M_Z)$. Relative to the next-to-leading order electroweak
corrections, the mixed QCD-electroweak corrections are found to be
approximately $18\%$ for $\alpha_s(M_Z)$. With respect to the leading order, we
observe a flat effect of the mixed QCD-electroweak corrections on the invariant
mass distribution of the lepton pairs with fixed QCD coupling. The $\phi$
distribution, due to the mixed QCD-electroweak corrections, follows a $(1-\cos
\phi)$ dependence.
