  We study rare radiative leptonic decays $B_{(s)}\to e^+e^-\gamma$ and
$B_{(s)}\to \mu^+\mu^-\gamma$ within relativistic quark model. In addition to
previous analysis we give the estimations of the branching ratios for four
values of the minimal photon energy, which correspond to photon selection
criteria of the Belle and LHCb detectors. We find out that the branching ratios
only slightly change. The highest values corresponding to $E^\gamma_{min}=80
\textrm{MeV}$ are ${\cal B}(\bar B^0_s\to e^+e^-\gamma)=18.5\times10^{-9}$ and
${\cal B}(B^0_s\to \mu^+\mu^-\gamma)=11.9\times10^{-9}$. We present the
distribution of the forward-backward asymmetry.
