We present an improved measurement of B meson lifetimes using
fully reconstructed B decays produced in p anti-p collisions at s**(1/2) = 1.8
TeV, using 114 pb-1 of data collected at the Collider Detector at Fermilab
(CDF). We obtain tau(B+/-) = 1.636 +/- 0.058 (stat) +/- 0.025 (syst) ps,
tau (B0) = 1.497 +/- 0.073 (stat) +/- 0.032 (syst) ps and for the lifetime
ratio: tau(B+/-)/tau(B0) = 1.093 +/- 0.066 (stat) +/- 0.028 (syst).