J. Tits introduced in his work on local characterizations of buildings [The geometric vein, The Coxeter Festschr., 519-547 (1982; Zbl 0496.51001)] the notion of a \(\sigma\)-homotopy group of an arbitrary chamber system. In Simon Stevin 58, 35-63 (1984; Zbl 0552.55012)] the author gave a method to calculate some \(\sigma\)-homotopy groups for arbitrary Coxeter complexes. The purpose of this paper is to give a criterium whether such a group is free.