Abstract: A new multivariate decision tree algorithm is proposed based on the conceptions of indiscernibility relation, compound operations, set operations and logical operation in set theory. It consists of five steps. Firstly, decision is classed according to the decision attribute value. Secondly, the attribute value is worked out according to the set intersection of the decision classes condition attribute. Thirdly, the independent decision condition attribute values are obtained according to each condition attribute field of the decision classification. Fourthly, multivariable decision rules are find out with compound operations of the decision classe condition sets. Finally, the OR operation is used to connect every decision rule in order to produce a complete rule. Experiment results demonstrate that the algorithm is effective. The time complexity results demonstrate that this algorithm has better time performance than rough sets algorithms, and no less than ID3 algorithm indeed.