Neutron diffraction studies on magnetic solids composed of axially elongated CoO X (X = Cl, Br, S, Se) octahedra show that the ordered magnetic moments of their high-spin Co (d , = / ) ions are greater than 3 μ , i.e., the spin moment expected for = / ions, and increase almost linearly from 3.22 to 4.45 μ as the bond-length ratio / increases from 1.347 to 1.659 where and are the Co-X and Co-O bond lengths, respectively. These observations imply that the orbital moments of the Co ions increase linearly from 0.22 to 1.45 μ with increasing the / ratio from 1.347 to 1.659. We probed this implication by examining the condition for unquenched orbital moment and also by evaluating the magnetic moments of the Co ions based on DFT+U+SOC calculations for those systems of the CoO X octahedra. Our work shows that the orbital moments of the Co ions are essentially quenched and, hence, that the observations of the neutron diffraction studies are not explained by the current theory of magnetic moments. This discrepancy between experiment and theory urges one to check the foundations of the current theory of magnetic moments as well as the current method of neutron diffraction refinements for ordered magnetic structures.