The q-chorded k-cycle inequalities are a class of valid inequalities for the clique partitioning polytope. It is known that for [Formula Presented], these inequalities induce facets of the clique partitioning polytope if and only if k is odd. Here, we characterize such facets for arbitrary k and q. More specifically, we prove that the q-chorded k-cycle inequalities induce facets of the clique partitioning polytope if and only if two conditions are satisfied: k=1 mod q, and if k=3q+1 then q=3 or q is even. This establishes the existence of many facets induced by q-chorded k-cycle inequalities beyond those previously known.