The lifetimes of the B 0 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 B 0 and B - mesons are partially reconstructed by identifying events containing a lepton with an associated D * + or D 0 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 * + - and 2856 D 0 - candidates yields the following results: τ B 0 =1.518+/-0.053+/-0.034<space>ps, τ B - =1.648+/-0.049+/-0.035<space>ps, τ B - /τ B 0 =1.085+/-0.059+/-0.018.