We note that with only a slight modification, Su’s proof on the fragments in \(k\)-critical \(n\)-connected graphs (see J. Graph Theory \(45 (2004), 281-297\)) can imply the following more general result: every non-complete \(W\)-locally \(k\)-critical \(n\)-connected graph has \(2k + 2\) distinct fragments \(F_1, F_2, \ldots, F_{2k+2}\) such that \(F_1 \cap W, F_2 \cap W, \ldots, F_{2k+2} \cap W\) are pairwise disjoint.