  A sensitive search for the lepton-number-violating decay $\Xi^-\to p
\mu^-\mu^-$ has been performed using a sample of $\sim10^9$ $\Xi^-$ hyperons
produced in 800 GeV/$c$ $p$-Cu collisions. We obtain $\mathcal{B}(\Xi^-\to p
\mu^-\mu^-)< 4.0\times 10^{-8}$ at 90% confidence, improving on the best
previous limit by four orders of magnitude.
