The magnetism of a recently synthesized trans-[Os^IVCl₄(κN₁-Hind)₂] complex (5d⁴-system), where Hind = 2H-indazole, was studied experimentally and theoretically. Relativistic CASSCF/CASPT2 calculations for this and model [Os^IVCl₆]²⁻ complexes were employed to understand the nature of the low-lying multiplets. It is found that despite strong metal–ligand covalency they are basically characterized by the total angular pseudo-momentum originating from the spin–orbit coupling of the ground-state spin S = 1 with the orbital pseudo-momentum = 1 of the Os^IV ion. The strong spin–orbit interaction also preserves the dominant = 0 character of the non-magnetic ground state in the trans-[Os^IVCl₄(κN₁-Hind)₂] complex despite significant deviation of the ligand environment of Os^IV from octahedral symmetry. At the same time the spin–orbit admixture of all multiplets arising from the t_2g⁴ strong-field electronic configuration is indispensable for the correct description of magnetic properties of Os^IV complexes. Moreover, based on ab initio calculations, we argue that the charge-transfer states play an important role in the magnetism of the present and probably other 5d complexes, a situation never encountered for 3d and 4f compounds.