Magnetism in transition metal compounds is usually considered starting from a description of isolated ions, as exact as possible, and treating their (exchange) interaction at a later stage. We show that this standard approach may break down in many cases, especially in 4d and 5d compounds. We argue that there is an important intersite effect-an orbital-selective formation of covalent metal-metal bonds that leads to an "exclusion" of corresponding electrons from the magnetic subsystem, and thus strongly affects magnetic properties of the system. This effect is especially prominent for noninteger electron number, when it results in suppression of the famous double exchange, the main mechanism of ferromagnetism in transition metal compounds. We study this mechanism analytically and numerically and show that it explains magnetic properties of not only several 4d-5d materials, including Nb 2 O 2 F 3 and Ba 5 AlIr 2 O 11 , but can also be operative in 3d transition metal oxides, e.g., in CrO 2 under pressure. We also discuss the role of spin-orbit coupling on the competition between covalency and magnetism. Our results demonstrate that strong intersite coupling may invalidate the standard single-site starting point for considering magnetism, and can lead to a qualitatively new behavior.double exchange | magnetism | transition metal compounds T ransition metal (TM) compounds present one of the main playgrounds in a large field of magnetism (1-3). Usually, when considering magnetic properties of these systems, one starts from the, as exact as possible, treatment of isolated TM ions or such ions in the surrounding of ligands, e.g., TMO 6 octahedra. A typical situation for a moderately strong crystal field is the one in which d electrons obey the Hund's rule, forming a state with the maximal spin. For a stronger crystal field low-spin states are also possible, but also in this case electrons in degenerate subshells, e.g., t 2g electrons, first form a state with maximal possible spin. Then, these large total spins interact by exchange coupling with the neighboring TM ions. This interaction, a superexchange for integer electron occupation (4), or a double exchange for partially filled d levels (5), is then treated using this starting point with this total spin of isolated ions, taking into account the hopping between sites (leading in effect to magnetic interaction) as a weak perturbation, which does not break the magnetic state of an ion.For heavier elements, such as 4d or 5d TM, one should also take into account the relativistic spin-orbit (SO) coupling, which couples the total spin S as dictated by the Hund's rule, with the (effective) orbital moment L. In any case, it is usually assumed that the "building blocks" for further consideration of the magnetic interactions are such isolated TM ions with the corresponding quantum numbers.However, especially when we go to heavier TM ions, such as 4d and 5d, also the spatial extent of the corresponding d orbitals increases strongly, and with it the effective d-d hopping, t (2). ...