  We calculate one-loop corrections to the decays of the next-to-lightest
neutralino $\tilde{\chi}_2^0$ into the lightest neutralino $\tilde{\chi}_1^0$
and two leptons; this includes diagrams where a real photon is emitted. In
cases where two-body decays $\tilde{\chi}_2^0 \to \tilde{l}^\pm_1 l^\mp \to
\tilde{\chi}_1^0 l^- l^+$ are kinematically allowed, we calculate these decays
both with and without the single-pole approximation, and find consistent
results. For example, for the minimal supergravity parameter set SPS1a, the
integrated partial widths (the branching ratios) for $\tilde{\chi}_2^0\to
\tilde{\chi}_1^0 l^- l^+ (l = e, \mu)$ are enhanced by about 15.5 (13.6)
percent by the one-loop corrections. We also study a scenario where $\tilde
\chi_2^0$ cannot undergo two-body decays, and find corrections to these
branching ratios of about 13.6 percent. Moreover, we study the dilepton
invariant mass ($M_{l^+ l^-}$) distribution, whose endpoint is often used in
analyses that aim to reconstruct (differences of) supersymmetric particle
masses at the LHC. The shape of this distribution is altered significantly by
the emission of hard photons. For example, for the SPS1a parameter set the peak
of the $M_{l^+ l^-}$ distribution is shifted by several GeV when these
contributions are included.
