This paper introduces tree multivalued dependencies (TMVDs) for XML documents by extending multivalued dependencies in relational databases and recent research about tree functional dependencies (TFDs). We show the existence of the TMVDs in XML documents that produce redundancies and update anomalies. Secondly, the precise definition of TMVDs is proposed, which is based on the tree structure and deep equality. Moreover, we introduce the concept of recomposition that is a reconstruction of an XML database by moving or adding nodes. The right side of TMVDs is characterized by single attribute and multiple attributes, for which there are different recompositions. In addition, the relationship between TFDs and TMVDs is investigated, and we demonstrate that a TMVD is a generalized TFD. Furthermore, we present a theorem showing the recomposition by TMVDs saves space. Finally, we exhibit a recomposition that is not equivalent to any relational data.