  The electronic and magnetic properties of Ba$_5$AlIr$_2$O$_{11}$ containing
Ir-Ir dimers are investigated using the GGA and GGA+SOC calculations. We found
that strong suppression of the magnetic moment in this compound recently found
in [J. Terzic {\it et al.}, Phys. Rev. B {\bf 91}, 235147 (2015)] is not due to
charge-ordering, but is related to the joint effect of the spin-orbit
interaction and strong covalency, resulting in the formation of metal-metal
bonds. They conspire and act against the intra-atomic Hund's rule exchange
interaction to reduce total magnetic moment of the dimer. We argue that the
same mechanism could be relevant for other $4d$ and $5d$ dimerized transition
metal compounds.
