  In view of precision studies of the Higgs sector at the Run II of the LHC,
the improvement of the accuracy of the theoretical prediction is becoming a
pressing issue. In this framework, we detail a calculation of the full
Next-to-Leading Order (NLO) electroweak corrections to Higgs boson decay into
four charged leptons, by considering the gold-plated channel H -> Z(*) Z(*) ->
2l 2l', l,l' = e, mu. We match the NLO corrections with a QED Parton Shower
(PS), in order to simulate exclusive multiple photon emission and provide novel
results at NLOPS electroweak accuracy. We compare our NLO predictions to those
of the program Prophecy4f and present NLOPS phenomenological results relevant
for Higgs physics studies, with particular attention to precision measurements
of the Higgs boson mass, spin-parity assignment and tests of the Standard
Model. Our calculation is implemented in a new code, Hto4l, which can be easily
interfaced to any generator describing Higgs boson production. As an example,
we provide illustrative results for Higgs production and decay in the process
gg -> H -> 4l using POWHEG with NLOPS accuracy in the production mode.
