The most precise determination of the neutron lifetime using the beam method was completed in 2005 and reported a result of τ(n)=(886.3±1.2[stat]±3.2[syst]) s. The dominant uncertainties were attributed to the absolute determination of the fluence of the neutron beam (2.7 s). The fluence was measured with a neutron monitor that counted the neutron-induced charged particles from absorption in a thin, well-characterized 6Li deposit. The detection efficiency of the monitor was calculated from the areal density of the deposit, the detector solid angle, and the evaluated nuclear data file, ENDF/B-VI 6Li(n,t)4He thermal neutron cross section. In the current work, we measure the detection efficiency of the same monitor used in the neutron lifetime measurement with a second, totally absorbing neutron detector. This direct approach does not rely on the 6Li(n,t)4He cross section or any other nuclear data. The detection efficiency is consistent with the value used in 2005 but is measured with a precision of 0.057%, which represents a fivefold improvement in the uncertainty. We verify the temporal stability of the neutron monitor through ancillary measurements, allowing us to apply the measured neutron monitor efficiency to the lifetime result from the 2005 experiment. The updated lifetime is τ(n)=(887.7±1.2[stat]±1.9[syst]) s.

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