  We report the results of a search for the rare baryonic decay modes B ->
Lambda Lambdabar, B -> Lambdabar p, B -> Lambdabar p pi, and B -> p pbar using
5.8M BBbar pairs collected with the CLEO detector. We see no statistically
significant signals in any of these modes and set 90% confidence level upper
limits on their branching fractions,
  B(B -> Lambda Lambdabar) < 3.9 \times 10^{-6},
  B(B -> Lambdabar p) < 2.6 \times 10^{-6},
  B(B -> Lambdabar p pi) < 1.3 \times 10^{-5}, and B(B -> p pbar) < 7.0 \times
10^{-6}.
