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In this paper, we consider two kinds of unordered tree matchings for evaluating tree pattern queries in XML databases. For the first kind of unordered tree matching, we propose a new algorithm, which runs in O(|D||Q|) time, where Q is a tree pattern and D is a largest data stream associated with a node of Q. It can also be adapted to an indexing environment with XB-trees being used to speed up disk access. Experiments have been conducted, showing that the new algorithm is promising. For the second of tree matching, the so-called strict unordered tree matching, we show that the problem is NP-complete by a reduction from the satisfiability problem.