  The lifetimes of B+ and B0 mesons have been measured using the entire sample
of 550,000 hadronic Z0 decays collected by the SLD experiment at the SLC
between 1993 and 1998. In this paper, we describe the inclusive analysis of the
350,000 hadronic Z0 decays collected in 1997-98 with the upgraded SLD vertex
detector. In this data period, a high statistics sample of 30903 (20731)
charged (neutral) vertices with good charge purity is obtained. The charge
purity is enhanced by using the vertex mass, the SLC electron beam polarization
(73% for 1997-8) and an opposite hemisphere jet charge technique. Combining the
results of this data sample with the results from the earlier data yield the
following preliminary values: $\tau_{B^+}=1.623\pm0.020($stat$)\pm0.034$(syst)
ps, $\tau_{B^0}=1.589\pm0.021($stat$)\pm0.043$(syst) ps, $\tau_{B^+}/\tau_{B^0}
= 1.037\pm^{0.025}_{0.024}($stat$) \pm0.024$(syst).
