Abstract
Using a sample of 9.6X 10(6)B (B) over bar meson pairs collected with the CLEO detector, we have fully reconstructed 135 B-0 --> psi(') K-S(0) and 526 B+ --> psi((')) K+ candidates with very low background. We fitted the psi((')) K invariant mass distributions of these B meson candidates and measured the masses of the neutral and charged B mesons to be M(B-0) = 5279.1 +/- 0.7[stat] +/- 0.3[syst] MeV/c(2) and M(B+) = 5279.1 +/- 0.4[stat] +/- 0.4[syst] MeV/c(2). The precision is a significant improvement over previous measurements.