The complete multipartite graph $K_{n(2t)}$ having n partite sets of size 2t, with $n;{geq};6$ and $t;{geq};1$, is shown to have a decomposition into gregarious 6-cycles, that is, the cycles which have at most one vertex from any particular partite set. Complete sets of differences of numbers in ${mathbb{Z}}_n$ are used to produce starter cycles and obtain other cycles by rotating the cycles around the n-gon of the partite sets.