Decomposition of bipartite graphs into closed trails

Let Lct(G) denote the set of all lengths of closed trails that exist in an even graph G. A sequence (t1,..., tp) of elements of Lct(G) adding up to |E(G)| is G-realisable provided there is a sequence (T1,..., tp) of pairwise edge-disjoint closed trails in G such that Ti is of length Ti for i = 1,..., p. The graph G is arbitrarily decomposable into closed trails if all possible sequences are G-realisable. In the paper it is proved that if a ⩾ 1 is an odd integer and Ma,a is a perfect matching in Ka,a, then the graph Ka,a-Ma,a is arbitrarily decomposable into closed trails.