The exchange interaction between magnetic adatoms on a metal surface is known to significantly influence the magnetic characteristics of the system. In present study we analyze the effect of the exchange interaction on the spin-dependent localization of the surface state. Our ab initio study of spin-polarized bound states arising at pairs of magnetic adatoms shows that both the position and the shape of the bound-state peak are strongly affected by the spin coupling in the system. Moreover we demonstrate that the spin splitting of the bound-state peak can serve as a suitable tool for probing the exchange coupling in the system. By the example of Co pairs on a Cu<111> surface at different interatomic separations, we demonstrate that the presence of the spin splitting of the bound-state peak is a signature of a ferromagnetic coupling while its absence signifies an antiferromagnetic configuration of the system spins. Also, the amount of splitting can be regarded as a measure of the interaction's strength.