  We study theoretically medium effects on $\Xi^-$ production in the ($K^-$,
$K^+$) reaction, using the optimal Fermi-averaging procedure which describes
the Fermi motion of a nucleon on the on-energy-shell $K^-p\to K^+\Xi^-$
reaction condition in nuclei. The result shows the strong energy and angular
dependence of the in-medium $K^-p\to K^+\Xi^-$ cross section,which affects
significantly the shape and magnitude of the production spectrum for $\Xi^-$
hypernuclear states in the ($K^-$, $K^+$) reaction on a nuclear target.The
application to the $\Xi^-$ quasi-free production via the ($K^-$, $K^+$)
reaction on a $^{12}$C target is also discussed in a Fermi gas model.
