The mean lifetime of the τ lepton is measured from a sample of Z→τ+τ− decays observed with the ALEPH detector at LEP in 1989 and 1990. A new technique is applied to the events containing two one-prong decays: the lifetime is measured from the observed correlation between the impact parameters and azimuthal angles of the two charged tracks. The lifetime is also determined from measured vertex displacements for three-prong decays and track impact parameters for one-prong decays. The combined results is ττ=291 ± 13 (stat) ±6 (syst.) fs.