Chunk decomposition is an aspect of problem solving that involves decomposing a pattern into its component parts in order to regroup them into a new pattern. Previous work suggests that the primary source of difficulty in chunk decomposition is whether a problem’s solution requires removing a part that is a meaningful perceptual pattern (termed a chunk) or not (a non-chunk). However, the role of spatial overlap (crossed relation or not) has been ignored in this line of research. Here, we dissociated the role of element type and crossed relation in chunk decomposition problems by employing a Chinese character transformation task. We replicated the finding that when the to-be-removed element is a non-chunk, the problem is more difficult to solve than when the element is a chunk. However, this result held only if the elements had no crossed relation. Relative to non-crossed relation, problems that involved removing elements that overlapped with the remaining character were more difficult to solve irrespective of the element type. We conclude that both element type and crossed relation can cause the difficulty of chunk decomposition and crossed relation plays more important role in preventing people from finding insightful ways to decompose chunk relative to element type.