A complete 3-uniform hypergraph of order n has vertex set V with |V | = n and the set of all 3-subsets of V as its edge set. A t-cycle in this hypergraph is v1, e1, v2, e2, . . . , vt, et, v1 where v1, v2, . . . , vt are distinct vertices and e1, e2, . . . , et are distinct edges such that vi, vi+1 ∈ ei for i ∈ {1, 2, . . . , t − 1} and vt, v1 ∈ et. A decomposition of a hypergraph is a partition of its edge set into edge-disjoint subsets. In this paper, we give necessary and sufficient

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... s for a decomposition of the complete 3-uniform hypergraph of order n into p-cycles, whenever p is prime.