We have used low temperature scanning tunneling spectroscopy and atomic manipulation to study the role of surface-state electrons in the Kondo effect of an isolated cobalt atom adsorbed on Ag(1 1 1). We show that the observed Kondo signature remains unchanged in close proximity of a monoatomic step, where the local density of states of the surface-state electrons is strongly perturbed. This result suggests a minor role for surface-state electrons in the Kondo effect of the cobalt adatom, compared to bulk electrons. A possible explanation for our findings is presented. (C) 2004 Elsevier B.V. All rights reserved.