New measurements of the neutron-neutron quasifree scattering cross section in neutron-deuteron breakup at an incident neutron energy of 10.0 MeV are reported. The experiment setup was optimized to evaluate the technique for determining the integrated beam-target luminosity in neutron-neutron coincidence cross-section measurements in neutron-deuteron breakup. The measurements were carried out with a systematic uncertainty of ±5.6%. Our data are in agreement with theoretical calculations performed using the CD-Bonn nucleon-nucleon potential in the Faddeev formalism. The measured integrated cross section over the quasifree peak is 20.5±0.5(stat)±1.1(sys)mb/sr2 in comparison with the theory prediction of 20.1mb/sr2. These results validate our technique for determining the beam-target luminosity in neutron-deuteron breakup measurements.