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We describe two constructions of (very) dense graphs which are edge disjoint unions of large induced matchings. The first construction exhibits graphs on N vertices with N 2 − o(N 2 ) edges, which can be decomposed into pairwise disjoint induced matchings, each of size N 1−o(1) . The second construction provides a covering of all edges of the complete graph K N by two graphs, each being the edge disjoint union of at most N 2−δ induced matchings, where δ > 0.076. This disproves (in a strongdoi:10.4171/jems/398 fatcat:oohcjpjonvepzemkyrc6hxffsu