The adsorption of hydrogen on the Co(10 (1) over bar0) surface has been studied by means of helium atom scattering. In agreement with previous results, three ordered adsorbate structures have been identified at 85 K: a c(2x4)4H, a (2x1)p2mg, and a (1x2) saturation phase. The surface structures were determined from a quantitative analysis of the corresponding He-diffraction spectra. The corrugation functions derived from the calculations reveal that in the c(2x4)4H phase the hydrogen atoms from zigzag and zagzig chains along every second close-packed row of the substrate, although the kind of occupied threefold sites cannot be determined from our data. In the (2x1)p2mg phase, hydrogen atoms are found to occupy the hcp-like sites, whereas the substrate's reconstruction in the (1x2) phase is of the pairing-row type. This means that hydrogen forms analogous structures on the Co(10 (1) over bar0) rather than on the structurally similar Ni(110) surface.