Compositional dependence of the induced uniaxial magnetic anisotropy constant K_ui was studied for rapidly quenched amorphous (Fe_1-xM_x)₇₇Si₁₀B₁₃, 0 ≤ x ≤ 0.7, (Fe_1-xCo_x)₇₇Si₁₀B₁₃, 0 ≤ x ≤ 1, Fe_100-xB_x, 14 ≤ x ≤ 19 and Co_100-xB_x, 17 ≤ x ≤ 30 alloys. In the former two alloy systems, the results can be explained by taking into account (i) insertion of metalloid atoms between ferromagnetic atoms and (ii) the directional ordering of magnetic atoms. While in the latter two binary alloy systems, the compositional dependence of K_ui can be explained roughly by (i).