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By a [Formula: see text]-decomposition of a graph G, we mean a partition of the edge set of G into p paths of length 4 and q cycles of length 4. In this paper, we give conditions for a [Formula: see text]-decomposition of the n-dimensional hypercube graph Qn for all possible values of p and q. In particular, we find the necessary and sufficient conditions for such decomposition in Qn when n is even, [Formula: see text] and n is odd, [Formula: see text]