We consider structure of the Cooper wave function for superconductivity in a surface layer. Broken space inversion at the surface results in lifted spin degeneracy and in two branches of the gapped energy spectrum as caused by the spin-orbit interaction. The pair wave function consists of a mixture of both singlet and triplet components. Anisotropy of the Knight shift measurable in the NMR experiments is calculated in the whole temperature regime. Implications for a few known experimental situations is briefly discussed.