[en] New accurate results of the neutron-proton spin-dependent total cross section difference Δσ_L(np) at the neutron beam kinetic energies 1.39, 1.69, 1.89 and 1.99 GeV are presented. Measurements were carried out in 2001 at the Synchrophasotron of the Veksler and Baldin Laboratory of High Energies of the Joint Institute for Nuclear Research. A quasi-monochromatic neutron beam was produced by break-up of extracted polarized deuterons. The deuteron (and hence neutron) polarization direction was flipped every accelerator burst. The vertical neutron polarization direction was rotated onto the neutron beam direction and longitudinally (L) polarized neutrons were transmitted through a large proton L-polarized target. The target polarization vector was inverted after 1-2 days of measurements. The data were recorded for four different combinations of the beam and target parallel and antiparallel polarization directions at each energy. A fast decrease of Δσ_L(np) with increasing energy above 1.1 GeV was confirmed. The structure in the Δσ_L(np) energy dependence around 1.8 GeV, first observed from our previous data, seems to be well pronounced. The new results are also compared with model predictions and with phase shift analysis fits. The Δσ_L quantities for isosinglet state I=0, deduced from the measured Δσ_L(np) values and the known Δσ_L(pp) data, are also given. The results were completed by the measurements of unpolarized total cross sections σ_0tot(np) at 1.3, 1.4 and 1.5 GeV and σ_0tot(nC) at 1.4 and 1.5 GeV. These data were obtained using the same apparatus and high intensity unpolarized deuteron beams were extracted either from the Synchrophasotron, or from the Nuclotron. (orig.)