[en] We are reporting on a new determination of sin²θ_W from the ratio of ν_μe to anti ν_μe scattering cross sections. A new detector designed for this purpose was exposed to the Wide Band Neutrino Beam of the 450 GeV CERN SPS. An analysis of data taken in 1987 and 1988 is presented based on 762 ν_μe and 1017 anti ν_μe events. From the ratio of σ(ν_μe) to σ(anti ν_μe) we determined sin²θ_W=0.233±0.012(stat)±0.008(syst) without radiative corrections. With radiative corrections for m_t=m_H=100 GeV we find sin²θ_W=0.232±0.012(stat)±0.008(syst). (orig.)