I present new results for the Standard-Model predictions of the differential decay rates for $H\to \ell^{+} \ell^{-} \gamma$, where $\ell=e, \mu$, and the forward-backward asymmetries defined in terms of the flight direction of the photon corresponding to the lepton momenta. The results depend on the selection criteria for the energies and invariant masses (i.e. the cuts) of the final state particles. For standard choices of these cuts the branching ratios $B(H\to e \bar e \gamma)=5.8\cdot 10^{-5}$ and $B(H\to \mu \bar \mu \gamma)=6.4\cdot 10^{-5}$ as well as the forward-backward asymmetries $\mathcal{A}^{(e)}_{\text{FB}}=0.343$ and $\mathcal{A}^{(\mu)}_{\text{FB}}=0.255$ have been found.