An improved measurement of the average b hadron lifetime is performed using a sample of 1.5 million hadronic Z decays, collected during the 1991–1993 runs of ALEPH, with the silicon vertex detector fully operational. This uses the three-dimensional impact parameter distribution of lepton tracks coming from semileptonic b decays and yields an average b hadron lifetime of 1.533 ± 0.013 ± 0.022 ps.