We present an improved direct measurement of the parity-violation parameter A(b) in the Z boson-b-quark coupling using a self-calibrating track-charge technique applied to a sample enriched in Z --> b (b) over bar events via the topological reconstruction of the B hadron mass. Manipulation of the Stanford Linear Collider electron-beam polarization permits the measurement of A(b) to be made independently of other Z-pole coupling parameters. From the 1996-1998 sample of 400 000 hadronic Z decays, produced with an average beam polarization of 73.4%, we find A(b) = 0.906 +/- 0.022(stat) +/- 0.023(syst).