Events from the e+e− → Zγ process with hard initial-state radiation collected with the L3 detector at centre-of-mass energies between 183 and 209 GeV are used to measure the mass of the Z boson. Decays of the Z boson into hadrons or muon pairs are considered and the Z mass is determined to be 91.272 ± 0.032(stat) ± 0.033(syst) GeV, in agreement with the value measured at the Z resonance. Alternatively, assuming this measured value of the Z mass, the method determines the LEP centre-of-mass energy, found to be 175 ± 68(stat) ± 68(syst) MeV lower than the nominal value.Facultad de Ciencias Exactas