  We study the production of $\Xi^-$-hypernuclei, $^{12}_{\Xi^{-}}$Be and
$^{28}_{\Xi^{-}}$Mg, via the ($K^-,K^+$) reaction within a covariant effective
Lagrangian model, employing the bound $\Xi^-$ and proton spinors calculated by
the latest quark-meson coupling model. The present treatment yields the
$0^\circ$ differential cross sections for the formation of simple s-state
$\Xi^-$ particle-hole states peak at a beam momentum around 1.0 GeV/c with a
value in excess of 1 $\mu$b.
