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The magnetic anisotropy of a rectangular Cu-O-Cu bond is investigated in second order of the spin-orbit interaction. Such a bond is characteristic for cuprates having edge sharing CuO 2 chains, and exists also in the Cu 3 O 4 plane or in ladder compounds. For a ferromagnetic coupling between the copper spins an easy axis is found perpendicular to the copper oxygen plaquettes in agreement with the experimental spin structure of Li 2 CuO 2. In addition, a pseudodipolar interaction is derived. Its estimation in the case of the Cu 3 O 4 plane (which is present for instance in Ba 2 Cu 3 O 4 Cl 2 or Sr 2 Cu 3 O 4 Cl 2) gives a value which is, however, two orders of magnitude smaller than the usual dipole-dipole interaction.