A 3-uniform hypergraph H is a pair (V,ε), where V is vertex set, ε, is a family of 3-subsets of V. If ε consists of all 3-subsets of V, H is a complete 3-uniform hypergraph on n vertices and is denoted by K n ( 3 ) . If V is the disjoint union of sets (so-called parts) V 1 and V 2 , and ε consists of all possible 3-subsets ζ of V 1 V 2 such that ζ V i , i = 1, 2, then H is a complete bipartite 3-uniform hypergraph and is denoted by K m , n ( 3 ) , if |V 1 | = m, |V 2 | = n. In this paper we show that following results on the decomposition of hypergraph into Hamiltonian cycles.(i)K n , n ( 3 ) has a decomposition into Hamiltonian cycles, n >= 2.(ii)all complete 3-uniform hypergraphs K 2 m ( 3 ) with 2 m vertices has a decomposition into Hamiltonian cycles, m >= 2.