The ground-state structures and energies of the bimetallic clusters ConCu55－n(n=0—55) were obtained by using the semi-empirical Gupta potential combined with a genetic algorithm. The ground-state geometries of those bimetallic clusters can be characterized by the basic Mackay icosahedron of the pure Co55 (Cu55) cluster. Beginning with n=0 (Cu55), the Cu atom(s) is(are) replaced in order and continuously by the Co atom(s) from the center to the surface and from the edge to the vertex. The ground-state structure depends on the number of the Co—Co bonds which have the largest energy, the number of the Co-Cu bonds with large energy and the average bond length of those bonds. Co13Cu42 is a magic cluster with an icosahedral core formed by 13 Co atoms, which plays a key role in the high stability of those bimetallic clusters.