To explore the crossover transition in the two-impurity Kondo problem, we calculate the differential conductance (dI / dV) corresponding to scanning tunneling spectroscopy (STS) measurements of a magnetic dimer adsorbed on a metal surface covered by a decoupling layer. With the aid of the numerical renormalization group (NRG) technique, we find that the peak structure of the dI / dV spectra near the Fermi level changes gradually as a function of the adatom separation and the coupling between the adatom localized spins and the metal surface conduction band. When the coupling becomes small, the peak disappears and, instead, a dip structure appears near the Fermi level. This dip structure is the manifestation of the strong antiferromagnetic correlation between the localized spins. We conclude that the gradual change of the dI / dV structure from a peak structure to a dip structure is an evidence of the crossover transition in the two-impurity Kondo problem. © 2010 Elsevier B.V. All rights reserved.