  The most precise determination of the neutron lifetime using the beam method
was completed in 2005 and reported a result of $\tau_n = (886.3 \pm 1.2
[\textrm{stat}] \pm 3.2 [\textrm{syst}])$ 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 have measured 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 was measured with a precision of 0.057 %, which
represents a five-fold improvement in the uncertainty. We have verified 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 $\tau_n = (887.7 \pm
1.2 [\textrm{stat}] \pm 1.9 [\textrm{syst}])$ s.
