[en] The lifetimes of B⁺ and B⁰ mesons have been measured using a sample of 400,000 hadronic Z⁰ decays collected by the SLD experiment at the SLC between 1993 and 1998. This inclusive topological measurement includes 250,000 hadronic Z⁰ decays collected since 1996 with teh SLD upgrade vertex detector. A high statistics sample of 30,028 (19,636) charged (neutral) vertices with good charge purity is obtained. The charge purity is enhanced by using the vertex mass, the SLC electron beam polarization (63% for 1993, 77% for 1994--6 and 73% for 1997--8) and an opposite hemisphere jet charge technique. Lifetime fits for the full data sample yield the following preliminary results: τ_B⁺ 1.686 ± 0.025(stat) ± 0.042(syst) ps, τ_b⁰ = 1.589 ± 0.026(stat) ± 0.055(syst) ps, τ_B⁺/τ_B⁰ = 1.061 ± 0.031/0.029(stat) ± 0.027(syst)