  Recently, the LHCb Collaboration performed first search for the rare
radiative $\Xi_{b}^{-}\rightarrow \Xi^{-}\gamma$ decay and put an upper limit,
${\cal B}(\Xi_{b}^{-}\to \Xi^{-}\gamma) < 1.3 \times 10^{-4}$, on its branching
ratio. The measurement agrees well with existing theory prediction using SU(3)
flavor symmetry method, but shows a slight tension with the previous prediction
from light-cone sum rules. Inspired by this, we investigate this decay as well
as other radiative decays of $\Xi_b^{0(-)}(\Xi^{'-}_{b})$ to $\Xi^{0(-)}$ and
$\Sigma^{0(-)}$ baryons using the form factors calculated from light-cone QCD
sum rules in full theory. we obtain $ {\cal B}(\Xi_{b}^{-}\to
\Xi^{-}\gamma)=1.08^{+0.63}_{-0.49} \times 10^{-5} $, which lies below the
upper limit set by LHCb and is consistent with flavor-symmetry driven
prediction. Our predictions on other channels may be checked in experiment and
by other phenomenological approaches.
