  The decay of the Standard Model Higgs boson into four leptons via a virtual
W-boson or Z-boson pair is one of the most important decay modes in the
Higgs-boson search at the LHC. We present the complete electroweak radiative
corrections of O(\alpha) to these processes, including improvements beyond
O(\alpha) originating from heavy-Higgs effects and final-state radiation. The
intermediate W- and Z-boson resonances are described (without any expansion or
on-shell approximation) by consistently employing complex mass parameters for
the gauge bosons (complex-mass scheme). The corrections to partial decay widths
typically amount to some per cent and increase with growing Higgs mass M_H,
reaching about 8% at M_H \sim 500 GeV. For not too large Higgs masses (M_H
<\sim 400 GeV) the corrections to the partial decay widths can be reproduced
within <\sim 2% by simple approximations. For angular distributions the
corrections are somewhat larger and distort the shapes. For invariant-mass
distributions of fermion pairs they can reach several tens of per cent
depending on the treatment of photon radiation. The discussed corrections have
been implemented in a Monte Carlo event generator called PROPHECY4F.
