The structure and relative stabilities of the different Sb4H+ clusters were investigated by means of high level ab initio calculations. For this purpose we have developed a split valence and an extended basis set for the treatment of Sb-containing compounds to be used with different effective core potentials available in the literature. The split-valence basis set reported seems to reproduce nicely the geometries and vibrational frequencies of different Sb-containing compounds, provided that electron correlation effects are included at the MP2 level. When the extended basis set is used, within the framework of the G2(ECP) theory, the atomization enthalpies of antimony derivatives are reproduced within +/- 3 kcal/mol. A systematic study of the Sb4H+ potential energy surface (PES) using these basis sets, showed that the global minimum is the result of the side protonation of the Sb-4 tetrahedral molecule. In this species the hydrogen is covalently attached to two Sb atoms through the formation of a three-centered delocalized bonding orbital similar to the one responsible for the stability of analogous P4H+ and As4H+ side-protonated species. This "nonclassical" structure is estimated to be 26 kcal/mol more stable than the classical corner-protonated form. The stability of these "nonclassical" structures increases as one descends in the group. Concomitantly, the gas-phase basicity also increases from P-4 to Sb-4, the latter being about 20 kcal/mol more basic than P-4 and about 14.5 kcal/mol more basic than As-4. In contrast with P-4 and As-4, the body-centered protonated species of Sb-4 is predicted to be a local minima of the PES. Similar trends have been found for BiH4+ species.