A new measurement of the forward-backward asymmetry in Z --> bbBAR dec
ays is presented. Hadrons from b decays are tagged using their long li
fetimes. The b quark charge and direction are reconstructed with a hem
isphere charge algorithm. The asymmetry and reconstructed b hemisphere
charge are measured in the 69 pb-1 of data collected by ALEPH during
1991, 1992 and 1993. They are used to extract sin2theta(w)eff, which i
s determined to be 0.2315 +/- 0.0016 (stat.) +/- 0.0009 (syst.), corre
sponding to an A(FB)b of 0.00992 +/- 0.0084 (stat.) +/- 0.0046 (stat.)
.