We report a density-functional study of some properties of the adsorption process of the NO molecule on small palladium clusters (n = 1-4). The interaction between NO and the Pd-n clusters is studied on various adsorption sites. Both, NO and Pd-n geometrical relaxations are taken into account. The significant conformational reconstruction of the metallic cluster upon NO adsorption induces a large decrease of the NO adsorption energy. Nevertheless, the N-O binding energy is strongly weakened when the molecule is adsorbed on the small Pd-n clusters due essentially to an electrostatic repulsion between both N and O atoms. The possible dissociation process of NO on Pd-4 cluster is then investigated within two processes: the NO molecule does not dissociate on Pd-4 with process (i) (dissociation of the isolated gas phase NO molecule followed by the adsorption of both nitrogen and oxygen atoms on the cluster). Process (ii) which presents three successive steps (adsorption of the NO molecule, dissociation of the NO molecule adsorbed on Pd-4, adsorption of the O atom on the cluster) is studied in details and we propose a reaction pathway locating transition states and intermediate species. The activation energy for process (ii) is high and the dissociation of the NO molecule on the Pd-4 cluster is thus highly improbable. (C) 2011 Elsevier B.V. All rights reserved.