  We calculate the neutrino energy emission rate due to singlet-state pairing
of protons in the neutron star cores taking into account the relativistic
correction to the non-relativistic rate. The non-relativistic rate is
numerically small, and the relativistic correction appears to be about 10 -- 50
times larger. It plays thus the leading role, reducing great difference between
the neutrino emissions due to pairing of protons and neutrons. The results are
important for simulations of neutron star cooling.
