)|V1||V2||V3| copies of K3. This fact and its various extensions are the key ingredients in most applications of Szemerédi's Regularity Lemma.To derive a similar results for r-uniform hypergraphs, r > 2, is a harder problem. In 1994, Frankl and Rödl developed a regularity lemma and counting argument for 3-uniform hypergraphs. In this paper, we exploit their approach to develop a counting argument for 4-uniform hypergraphs.