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.
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