In the new experiment , performed at LANL by the UCNtau Collaboration with their magnetic trap for ultracold neutrons, the Collaboration has achieved the most precise measurement of the neutron lifetime tau = 877,75 +- 0,34 s. In comparison with the previous experiment, the statistical and the systematic uncertainties have been reduced to values less than the above quoted level, approaching now the theoretical precisions of calculations in beta-decay within the Standard Model of elementary particles.