A new algorithm of attribute reduction based on boolean matrix computation is proposed in this paper. The method compresses the valid information stored in table into a binary tree, at the same time deleting the invalid information and sharing a branch about the same prefix information. Some relative concepts such as local core attributes, local attribute reduction and global core attributes, global attribute reduction are introduced. The conclusions that the global core set is the union of all local core sets and the global attribute reduction sets are the union of respective local attribute reduction sets are proved. The attribute reduction steps of the algorithm are presented. At last, The correctness and effectiveness of the new algorithm are also shown in experiment and in an example.