  A simple method to explore the interaction of antihyperons in nuclei by
exclusive hyperon-antihyperon pair production close to threshold in antiproton
nucleus interactions is proposed. Due to energy and momentum conservation
event-by-event transverse momentum correlations of the produced hyperons and
antihyperons contain information on the difference between their potentials. A
schematic Monte Carlo simulation is used to illustrate the sensitivities of the
proposed method for the reaction 1.66GeV/c antiproton+$^{12}$C $\to
{\Lambda\bar{\Lambda}}$. For produced D-meson pairs at 6.7GeV/c the sensitivity
of the transverse momenta correlation will probably be to small to deduce
differences between the potentials for D$^+$ and D$^-$ mesons. However, for
$\Xi\bar{\Xi}$ pairs produced at 2.9GeV/c the asymmetry is sufficiently
sensitive to predicted differences between the $\Xi$ and $\bar{\Xi}$
potentials.
