We present a calculation of the mass of the S-1(0) pseudoscalar (b) over ba
r c (B-c) state using a non-perturbative measurement from quenched lattice
QCD, We find M-Bc = 6.386(9)(98)(15) GeV where the first error is statistic
al, the second systematic due to the quark mass ambiguities and quenching a
nd the third the systematic error due to the estimation of mass of the eta(
b). (C) 1999 Published by Elsevier Science B.V. All rights reserved.