  We report results of a search for the charmless two-body baryonic decays B^0
\to p \bar{p}, B^0 \to \Lambda \bar{\Lambda}, and B^+\to p \bar{\Lambda} based
on the analysis of a 140 fb^{-1} data sample. We set 90% confidence level upper
limits on their branching fractions: B(B^0 \to p \bar{p}) < 4.1 x 10^{-7},
B(B^0 \to \Lambda \bar{\Lambda}) < 6.9 x 10^{-7}$, and B(B^+ \to p
\bar{\Lambda}) < 4.9 x 10^{-7}.
