AbstractLet G be a graph whose edges are colored with k colors, and be a k‐tuple of graphs. A monochromatic ‐decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a monochromatic copy of in color i, for some . Let be the smallest number ϕ, such that, for every order‐n graph and every k‐edge‐coloring, there is a monochromatic ‐decomposition with at most ϕ elements. Extending the previous results of Liu and Sousa [Monochromatic ‐decompositions of graphs, J Graph Theory 76 (2014), 89–100], we solve this problem when each graph in is a clique and is sufficiently large.