A neutron spectrometer based on stilbene crystals has been developed by the Flerov Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research (Dubna, Russia). The timing resolution is determined as a function of the signal amplitude (sigma T = 0.18 ns at an amplitude of 1 MeV in the electron equivalent). The measured energy resolution of the detecting modules for gamma rays is sigma E/E = 4.5% at E = 1 MeV. The quality of the n-gamma discrimination is investigated. It is shown that reliable discrimination is possible, beginning with a deposited energy of 100 keV in the electron equivalent, which corresponds to the kinetic energy of recoil protons of ~ 700 keV. The neutron spectrometer helps to significantly expand the experimental capabilities and to carry out correlation experiments with radioactive beams on the ACCULINNA-2 fragment separator at a new level of quality.