In a recent paper [1] Maynard answered a question of Harary and Manvel [2] about the reconstruction of \(square-celled \;animals\). One of his results relied on a general algebraic approach due to Alon, Caro, Krasikov, and Roditty [3]. Applying arguments of a more combinatorial nature we improve this result and give an answer to a question raised by him in [1].