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Many well-known interconnection networks, such as kary n-cubes, recursive circulant graphs, generalized recursive circulant graphs, circulant graphs and so on, are shown to belong to the family of cycle composition networks. Recently, various studies about mutually independent Hamiltonian cycles, abbreviated as MIHC's, on interconnection networks are published. In this paper, using an improved construction method, the authors obtain MIHC's on cycle composition networks with a much weaker condition than the known result. In fact, they established the existence of MIHC's in the cycle composition networks and the result is optimal in the sense that the number of MIHC's they constructed is maximal.
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