  We evaluate two-body decay modes of neutralinos in the Minimal Supersymmetric
Standard Model with complex parameters (cMSSM). Assuming heavy scalar quarks we
take into account all two-body decay channels involving charginos, neutralinos,
(scalar) leptons, Higgs bosons and Standard Model gauge bosons. The evaluation
of the decay widths is based on a full one-loop calculation including hard and
soft QED radiation. Of particular phenomenological interest are decays
involving the Lightest Supersymmetric Particle (LSP), i.e. the lightest
neutralino, or a neutral or charged Higgs boson. For the chargino/neutralino
sector we employ two different renormalization schemes, which differ in the
treatment of the complex phases. In the numerical analysis we concentrate on
the decay of the heaviest neutralino and show the results in the two different
schemes. The higher-order corrections of the heaviest neutralino decay widths
involving the LSP can easily reach a level of about 10-15%, while the
corrections to the decays to Higgs bosons are up to 20-30%, translating into
corrections of similar size in the respective branching ratios. The difference
between the two schemes, indicating the size of unknown two-loop corrections,
is less than order(0.1%). These corrections are important for the correct
interpretation of LSP and Higgs production at the LHC and at a future linear
e+e- collider. The results will be implemented into the Fortran code FeynHiggs.
