Cerium hexaboride is an antiferromagnetic metal with a Ne´el temperature of 3°K. The high‐temperature inverse susceptibility of this material is observed to decrease with decreasing temperature more rapidly than would be expected from a Curie‐Weiss law. Since the temperature at which this deviation appears is much higher than the eventual ordering temperature, short‐range ordering effects should be negligible. Also, it can be shown that crystal‐field effects alone cannot produce such a decrease in &khgr;−1. In this paper we offer a possible mechanism which explains this behavior. Basically, we assume that the Ce&sngbnd;Ce exchange arises through an indirect exchange involving the conduction electrons. We visualize the conduction electrons as moving in the spaces between the boron complexes so that the magnitude of thes‐fexchange will be different for the different crystal‐field states of cerium. In a cubic field the2F5/2state of Ce3+splits into a &Ggr;7and a &Ggr;8. Low‐temperature measurements of the saturation moment indicate that the &Ggr;7state lies lowest. Therefore, as the temperature decreases, the &Ggr;8state, which protrudes into the space between the borons and, hence, contributes strongly to thes‐fexchange, is frozen out, leaving only the weakly coupled &Ggr;7state.