Let \(K_ r(n)\) be a complete r-partite hypergraph with n vertices. By \(f_ r(n)\) is denoted the minimal number q of pairwise edge-disjoint r- partite complete r-uniform hypergraphs which cover all edges of \(K_ r(n).\) In the paper is given an asymptotic value of the \(f_ r(n)\). For every fixed \(r\geq 1\) exist two positive numbers \(c_ 1(r)\) and \(c_ 2(r)\) such that \[ c_ 1\cdot n^{[r/2]}\leq f_ r(n)\leq c_ 2\cdot n^{[r/2]} \] for all \(n\geq r.\) The lower bound is proved using some methods of linear algebra and the upper bound is constructive. The construction is sharp for the case \(r=2,3\) where \(f_ 2(n)=n-1\) and \(f_ 3(n)=n-2\).