Co-(Pr, Nd, Gd, Dy, Er) amorphous binary alloy films were fabricated by evaporation technique. Perpendicular magnetic anisotropy constants, K⊥, and magnetostriction, λ, were systematically examined. For Dy-Co alloy films, the maximum value of K⊥ at 77K, 9×106erg/cm3, was obtained at 25 at.%Dy. For Gd-Co films, K⊥ were nearly equal to zero, independent of Gd concentration. In Er-Co films, K⊥ at 77K showed the minimum value of -2.5×106erg/cm3 around 19 at.%Er. λ for Gd-Co films monotonously decreased from 60×10 -6 at 17.1 at.%Gd to 15×10-6 at 55.1 at.%Gd. For Dy-Co films, the maximum value of λ was found to be about 220×10-6at 31.5 at.%Dy. In Er films, the sign of λ changed around 17 at.%Er. Change of K⊥max (77 K) for each alloy film against various RE elements was found to be similar to that of the uniaxial anisotropy expected from each RE single ion in Gd based crystal. This fact suggests that the mechanism of the perpendicular magnetic anisotropy of these amorphous films is well explained by the single ion model of RE elements, together with the local atomic order of RE atoms.