  The lifetimes of the Bbar0 and B- mesons are measured using a sample of about
four million hadronic Z decays collected from 1991 to 1995 with the ALEPH
detector at LEP. The data sample has been recently reprocessed, achieving a
substantial improvement in the tracking performance. Semileptonic decays of
Bbar0 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 D0l-
candidates yields the following results: tauBbar0 = 1.518 +- 0.053 +- 0.034 ps,
tauB = 1.648 +- 0.049 +- 0.035 ps, tauB-/tauBbar0 = 1.085 +- 0.059 +- 0.018.
