We have performed semi-empirical LCAO calculations of the electronic structure of the Cu(1 1 0)-p(2 x 1)O surface. This has been done accounting for the Cu-Cu interactions by means of a recently proposed set of parameters, which give very good results for the bulk as well as for the surfaces of lowest Miller indices. Furthermore, the O-O interactions, which have been neglected in the preceding similar studies, have been taken into account. The resulting surface bands are in very good agreement with the overall set of the available experimental data. Several issues concerning the physical properties of this surface are addressed in the present paper: the changes induced on the clean surface bands by the adsorption and the reconstruction; the arrangement of the Cu and O atoms in the added rows; the position of the p(y) antibonding band of the oxygen. In particular, we have found that the latter has an energy of -0.2 eV at the Y point. This result confirms an experimental indication in the same direction previously reported by Courths et al. [R. Courths, S. Hilfher, P. Kemkes, G. Wiesen, Surf. Sci. 376 (1997) 43]