Detailed knowledge of the type and strength of pair interactions between high-spin metal ions is paramount to the understanding and design of molecular magnetic materials. In this work, the anisotropic magnetic interactions in a beta-diketonate-alkoxide iron(III) dimer compound, [Fe-2(OCH3)(2)(dbm)(4), Hdbm = dibenzoylmethane] (Fe-2) have been investigated by single crystal electron paramagnetic resonance (EPR) in the W-band (at 95 GHz). The diamagnetic substitution method was employed using the isomorphous gallium(III)-based compound doped with iron(III) to produce Ga-Fe dimers (GaFe). The single-ion zero-field splitting (ZFS) tensor could be separately determined in GaFe with the iron ion in a local environment quasi-identical to the one in Fe2. Its principal directions are found to point in arbitrary directions, uncorrelated with the Fe-O bonds. The Fe2 EPR spectra consist of transitions within the lowest multiplet states S = 1, 2, 3, which were analyzed using the full Spin Hamiltonian description of all exchange coupled pair of s = 5/2 spins. The anisotropic spin-spin interaction tensor of Fe2 possesses a principal axis close to the Fe-Fe direction and was shown to arise both from through-space (dipolar) and through-bond (anisotropic exchange) contributions. The latter involves a rhombic component J(E) = (J(X) - J(Y))/2 ca. 0.093 cm(-1) of magnitude comparable to the dipolar interaction, and even to the rhombic part of the single-ion ZFS (E = 0.097 cm(-1)). Our results show that the anisotropic exchange, usually neglected for S-type ions, is significant for the anisotropic interactions in exchange-coupled iron(III) clusters, including the Fe-4 and Fe-8 families of single-rnolecule magnets and the antiferromagnetic iron wheels.