Nonelastic cross sections of nuclei for fast neutrons have been measured by using a new method of analysis for the conventional sphere-transmission data. The multiple-scattering correction has been made by a simple polynomial extrapolation formula, while the error caused by energy loss in elastic collisions has been corrected by the two-bias method developed by the authors. The latter method enables one to measure inelastic neutrons in the presence of elastic neutrons, without any loss in relative efficiencies. For other minor errors, corrections have been made in the usual way. The nonelastic cross sections for 14.8-MeV neutrons of C, O, Al, Cu, Cd, Sn, Ce, W, and Pb nuclei have been measured, respectively, as 0.55±0.02, 0.85±0.04, 0.94±0.03, 1.46±0.03, 1.85±0.04, 1.91d=0.04, 2.03±0.08, 2.44±0.06, 2.50±0.05 b/nucleus. The results have been interpreted in terms of local and nonlocal optical models.