  The production of $\Xi(1321)^{-}$ and $\overline{\Xi}(1321)^{+}$ hyperons in
inelastic p+p interactions is studied in a fixed target experiment at a beam
momentum of 158 GeV/textit{c}. Double differential distributions in rapidity y
and transverse momentum $p_{T}$ are obtained from a sample of 33M inelastic
events. They allow to extrapolate the spectra to full phase space and to
determine the mean multiplicity of both $\Xi^{-}$ and $\overline{\Xi}^{+}$. The
rapidity and transverse momentum spectra are compared to transport model
predictions. The $\Xi^{-}$ mean multiplicity in inelastic p+p interactions at
158~\GeVc is used to quantify the strangeness enhancement in A+A collisions at
the same centre-of-mass energy per nucleon pair.
