  Based on reflection symmetry in the reaction plane, it is shown that
measuring the transverse spin-transfer coefficient $K_{yy}$ in the $\bar{K}N
\to K\Xi$ reaction directly determines the parity of the produced cascade
hyperon in a model-independent way as $\pi_\Xi =K_{yy}$, where $\pi_\Xi =\pm 1$
is the parity. This result based on Bohr's theorem provides a completely
general, universal relationship that applies to the entire hyperon spectrum. A
similar expression is obtained for the photoreaction $\gamma N \to K K \Xi$ by
measuring both the double-polarization observable $K_{yy}$ and the photon-beam
asymmetry $\Sigma$. Regarding the feasibility of such experiments, it is
pointed out that the self-analyzing property of the $\Xi$'s can be invoked,
thus requiring only a polarized nucleon target.
