  We formulate ``Witten'' matching conditions for confining gauge theories. The
conditions are analogous to 't Hooft's, but involve Witten's global SU(2)
anomaly. Using a group theoretic result of Geng, Marshak, Zhao and Okubo, we
show that if the fourth homotopy group of the flavor group $H$ is trivial
($\Pi_4(H) = 0$) then realizations of massless composite fermions that satisfy
the 't Hooft conditions also satisfy the Witten conditions. If $\Pi_4 (H)$ is
nontrivial, the new matching conditions can yield additional information about
the low energy spectrum of the theory. We give a simple physical proof of Geng,
et. al.'s result.
