A large uniaxial magnetic anisotropy Ku of about 2× 107 erg cm3 was obtained in Co-(20-30) at. % Pt perpendicular films deposited on Ru seed layers. The films showed good c -axis orientation perpendicular to the film plane, and no evidence of a Co3 Pt -type-ordered structure was found in the X-ray-diffraction patterns. The value of Ku (the sum of the first- and second-order terms of uniaxial anisotropy, Ku1 and Ku2) increased as the thickness of the CoPt layer decreased, and reached about 2× 107 erg cm3 at 2 nm (Co-20 at. % Pt films) or 5 nm (Co-(25-30) at. % Pt films). The ratio of Ku2 to Ku1 was 0.16 in 40 nm films, but reduced to less than 0.03 for thicknesses below 5 nm. The experimental results suggest that, besides the surface anisotropy, the increase in Ku on reducing the thickness is mostly related to the reduction of the hcp-CoPt lattice ca ratio, probably due to epitaxial growth of CoPt on the Ru seed layer.