An improved measurement of the forward-backward asymmetry in Z --> b (
b) over bar decays is presented, based on a sample of 4.1 million hadr
onic Z decays collected by ALEPH between 1991 and 1995. Data are analy
sed as a function of polar angle of the event axis and b purity. The e
vent tagging efficiency and mean b-jet hemisphere charge are measured
directly from data. From the measured forward-backward jet charge asym
metry, the b quark asymmetry at root s= m(Z) is determined to be: A(FB
)(b) = 0.1017 +/- 0.0032(syst.) +/- 0.0032(syst.). In the context of t
he Standard Model this corresponds to a value of the effective weak mi
xing angle of sin(2) theta(W)(eff)= 0.23109 +/- 0.00096. (C) 1998 Publ
ished by Elsevier Science B.V, All rights reserved.