The lifetimes of the B0 and B- mesons are measured using a sample of about four million hadronic Z decays collected from 1991 to 19 95 with the ALEPH detector at LEP. The data sample has been recently reprocessed, achieving a substantial improvement in the tracking performance. Semileptonic decays of B0 and B- mesons are partially reconstructed by identifying events containing a lepton with an associated D* or D0 meson. The proper time of the B meson is estimated from the measured decay length and the momentum of the D-lepton system. A fit to the proper time of 1880 D* l- and 2856 D0 l- candidates yields the following results: tau B0 = 1.518 +- 0.053 +- 0.034 ps, tau B- = 1.648 +- 0.049 +- 0.035 ps, tau B- / tau B0 = 1.085 +- 0.059 +- 0.018
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