  Recently the LHCb collaboration put the upper limit on the $\Xi^{-}_{b}
\rightarrow \Xi^{-}\gamma$ decay branching ratio $Br(\Xi^{-}_{b} \rightarrow
\Xi^{-}\gamma)< 1.3\times 10^{-4}$. The measured value is below the light-cone
sum rule prediction. In this paper the rare radiative decay of the
$\Xi^{-}_{b}$ baryon is studied in the framework of the relativistic quark
model based on the quasipotential approach and QCD. The decay form factors are
calculated with the comprehensive account of the relativistic effects. The
obtained result for the branching ratio is found to be below the upper limit
set by LHCb and is consistent with theoretical predictions based on the SU(3)
flavor-symmetry, light-front quark model and light-cone QCD sum rules in full
theory within theoretical uncertainties.
