Abstract The BCS theory is extended to the case of some copper-oxide superconductors with two crystal structure features: the Cu O layers in which the superconducting current mainly flows have the asymmetric nearest neighborhod and they are grouped in pairs. The symmetry of such structures allows the antipyroelectricity phenomenon, i.e. the existence of intracrystalline electric field perpendicular to the layers and oppositely directed in adjacent layers. The superconductivity of one double-electron layer is considered: the order parameter matrix and the quasiparticle excitation spectrum are obtainedn and finite value of spin susceptibility at zero temperature is found. Apart from that it is esrablshed that due to lifting of spin degeneracy a novel spin contribution to the Hall effect in the normal state appears.