In [8], it is shown that the complete multipartite graph

having n partite sets of size 2t, where

, has a decomposition into gregarious 6-cycles if

or 4 (mod 6). Here, a cycle is called gregarious if it has at most one vertex from any particular partite set. In this paper, when

or 3 (mod 6), another method using difference set is presented. Furthermore, when

(mod 6), the decomposition obtained in this paper is

, in the sense that it is invariant under the mapping which keeps the partite set which is indexed by

fixed and permutes the remaining partite sets cyclically.