Magnetic atoms at surfaces may provide the ultimate paradigm of a solid-state magnetic memory exhibiting either classical , or quantum , behaviour. Individual atoms, however, are difficult to arrange in regular patterns1,2,3,4, . Moreover, their magnetic properties are dominated by interaction with the substrate, which, as in the case of Kondo systems, often leads to a decrease or quench of their local magnetic moment , . Here we show that the supramolecular assembly of Fe and 1,4-benzenedicarboxylic acid molecules on a Cu surface results in ordered arrays of high-spin mononuclear Fe centres on a 1.5 nm square grid. Lateral coordination with the molecular ligands yields unsaturated yet stable coordination bonds, which allow for the chemical modification of the electronic and magnetic properties of the Fe atoms independently from the substrate. The easy magnetization direction of the Fe centres can be switched by oxygen adsorption, thus opening a way to control the magnetic anisotropy in supramolecular layers akin to that employed in metallic thin films , , , .