If s1, s2, …, st are integers such that n − 1 = s1 + s2 + ··· + st and such that for each i (1 [les ] i [les ] t), 2 [les ] si [les ] n − 1 and sin is even, then Kn can be expressed as the union G1 ∪ G2 ∪ ··· ∪ Gt of t edge-disjoint factors, where for each i, Gi is si-regular and si-connected. Moreover, whenever si = sj, Gi and Gj are isomorphic.