  This article reports an improved independent measurement of neutrino mixing
angle $\theta_{13}$ at the Daya Bay Reactor Neutrino Experiment. Electron
antineutrinos were identified by inverse $\beta$-decays with the emitted
neutron captured by hydrogen, yielding a data-set with principally distinct
uncertainties from that with neutrons captured by gadolinium. With the final
two of eight antineutrino detectors installed, this study used 621 days of data
including the previously reported 217-day data set with six detectors. The
dominant statistical uncertainty was reduced by 49%. Intensive studies of the
cosmogenic muon-induced $^9$Li and fast neutron backgrounds and the
neutron-capture energy selection efficiency, resulted in a reduction of the
systematic uncertainty by 26%. The deficit in the detected number of
antineutrinos at the far detectors relative to the expected number based on the
near detectors yielded $\sin^22\theta_{13} = 0.071 \pm 0.011$ in the
three-neutrino-oscillation framework. The combination of this result with the
gadolinium-capture result is also reported.
