A method of measurements of the environmental neutron background at the Baksan Neutrino Observatory of the INR RAS are described. Measurements were done by using of a proportional counter filled with mixture of Ar(2 at)+$^3$He(4 at). The results obtained at the surface and the underground laboratory of the BNO INR RAS are presented. It is shown that a neutron background in the underground laboratory at the 4900 m w.e. depth is decreased by $sim 260$ times without any special shield in a comparison with the Earth surface. A neutron flux density in the 5-1323.5~cm air height region is constant within the determination error and equal to $(7.1pm0.1_{rm{stat}}pm0.3_{rm{syst}})times10^{-3}$ s$^{-1}cdot$cm$^{-2}$.
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