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 numer
ically small, and the relativistic correction appears to be about 10-50 tim
es larger. It plays thus the leading role, reducing great difference betwee
n the neutrino emissions due to pairing of protons and neutrons. The result
s are important for simulations of neutron star cooling.