  We calculate the magnetic dipole and electric quadrupole moments associated
with the radiative $\Omega_{Q}^{*}\rightarrow\Omega_{Q}\gamma$ and
$\Xi_{Q}^{*}\rightarrow\Xi^{\prime}_{Q}\gamma$ transitions with $Q=b$ or $c$ in
the framework of light cone QCD sum rules. It is found that the corresponding
quadrupole moments are negligibly small while the magnetic dipole moments are
considerably large. A comparison of the results on the considered multipole
moments as well as corresponding decay widths with the predictions of the
vector dominance model is performed.
