High-resolution angle-resolved photoabsorption spectra of HBr below the Br $3d$ ionization thresholds were recorded in the total ion yield. By applying adequate selection rules for excitations from core holes with a strong spin-orbit interaction, we demonstrate for the ${3d}_{{j,m}_{j}}^{\ensuremath{-}1}\mathrm{nl}\ensuremath{\lambda}$ states that this technique is a powerful tool to study the multiplet splitting of the Rydberg states into the different sublevels ${M}_{j}.$ We report a multiplet splitting of $\ensuremath{\cong}50 \mathrm{meV}$ between the ${M}_{j}=1$ and ${0}^{+}$ substates of the ${3d}_{5/2,1/2}^{\ensuremath{-}1}5s\ensuremath{\sigma}$ and ${3d}_{3/2,1/2}^{\ensuremath{-}1}5s\ensuremath{\sigma}$ excitations. As a consequence of this observation, an assignment of the photoabsorption spectrum different to those of earlier studies is derived in the low-energy region. In addition, the orientation parameter ${\ensuremath{\beta}}_{m}$ is derived from the spectra.