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The origin of the striking magnetic anisotropy of cobaltous oxide (CoO) is investigated by model calculations. A key feature of the electronic structure of the antiferromagnetic compound is the accommodation of Co 3d electrons in the (111) Co planes, with parallel and antiparallel intra- and interplane spin orientations and reminiscent of Cu 3d electrons in the CuO2 planes in high-temperature superconductors. The strong correlations of the Co 3d electrons lead to a picture intermediate between traditional crystal-field and itinerant-electron descriptions of the magnetic anisotropy. Using a simple configuration-interaction approach, we analyze the effect of 3d8-3d6 bonds and their interplay with 3d7-3d7 configurations.