[en] A detailed Monte Carlo simulation of neutrino fluxes of atmospheric origin is made taking into account the muon polarization effect on neutrinos from muon decay. There still remains a significant discrepancy between the calculated (ν_e + antiν_e)/(ν_μ + antiν_μ) ratio and that observed by the Kamiokande group, which can be explained by three neutrino oscillations. However, the ratio evaluated at the Frejus site and the total event number calculated for IMB-1 show good agreement with the data. Comparing out result with the previous Monte Carlo calculation by Barr et al., we find that the two calculations agree within 20 % for the magnitude of neutrino fluxes and 5 % for the (ν_e + antiν_e)/(ν_μ + antiν_μ) ratio. This paper is the revised version for correcting computational errors in the previous preprint, INS-Rep.-807. (J.P.N.)