A new limit is presented on the axion-like monopole-dipole P, T-non-invariant interaction in a range (10 −4 -1) cm. The spin-dependent nucleon-nucleon potential between neutrons and nucleons of the walls of the cavity containing ultra-cold neutrons should affect the neutron depolarization probability at their reflection from the walls. The limit is obtained from existing data on the ultra-cold neutron depolarization probability per one collision with the walls.