The spin-spin dependence of the total cross section of /sup 59/Co for neutrons was measured at seven energies. A polarized neutron beam with energies of 8.2, 11.1, 12.8, and 14.1 MeV from the /sup 2/H(d,n)/sup 3/He reaction and of 23.0, 27.5, and 30.6 MeV from the /sup 3/H(d,n)/sup 4/He reaction was transmitted through a cobalt sample. The cobalt target was cooled with a /sup 3/He-/sup 4/He dilution refrigerator and polarized in a magnetic field. The transmission rates of the neutrons were compared for parallel and antiparallel spin orientations. The values obtained for the spin-spin cross section are much smaller than those found below 3 MeV. Deduced strengths of spin-spin terms in the optical model are in the range of 1 MeV. This is of the same order of magnitude as estimated from microscopic calculations.