Ab initio Coupled-Cluster calculations with single and double excitations and perturbative correction to the triple, CCSD(T), have been carried out for the high-spin electronic state, ((5) A(2)), of the copper cluster Cu-4 in its tetrahedral arrangement. Like alkali metals clusters, tetrahedral Cu-4 presents a bound quintet state, i.e., a situation where all the valence electrons are unpaired. This rather exotic wavefunction, also known as no-pair bonding state, is examined in detail. The influence of the basis set is also analyzed, as well as the importance of the core correlation and the effect of the basis-set superposition errors. (C) 2011 Elsevier B.V. All rights reserved.