  We consider the model of superconducting pairing with the energy gap function
which is odd over $k-k_{F}$.\ In this case superconductivity is possible even
in the presence of an arbitrarily large point-like repulsion between
electrons,\ which is attractive for the theory of high-temperature
superconductors.\ We discuss mainly a model pairing interaction for which the
BCS equations can be solved exactly,\ allowing the complete analysis of the
interplay of the usual (``even'') and ``odd'' pairing,\ depending on the
coupling constant.\ We also show that the normal impurities (disorder) lead to
a rapid degradation of the ``odd'' pairing,\ which is even more rapid than in
case of magnetic impurities in traditional superconductors.
