  A sensitive search for the rare decays \Omega^- \to \Lambda \pi^- and \Xi^0
\to p \pi^- has been performed using data from the 1997 run of the HyperCP
(Fermilab E871) experiment. Limits on other such processes do not exclude the
possibility of observable rates for |\Delta S| = 2 nonleptonic hyperon decays,
provided the decays occur through parity-odd operators. We obtain the
branching-fraction limits B(\Omega^- \to \Lambda \pi^-)< 2.9 x 10^{-6} and
B(\Xi^0 \to p \pi^-)< 8.2 x 10^{-6}, both at 90% confidence level.
