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Actual data sets are often incomplete because of various kinds of reason. Although many algorithms for classification have been proposed, most of them deal with complete data. So methods of constructing classifiers for incomplete data deserve more attention. By analyzing main methods of processing incomplete data for classification, this paper presents a selective Bayes classifier for classifying incomplete data. The proposed algorithm needs no assumption about data sets that are necessary for previous methods of processing incomplete data. Experiments on twelve benchmark incomplete data sets show that this algorithm can greatly improve the accuracy of classification. Furthermore, it can also sharply reduce the number of attributes and so can greatly simplify the data sets and classifiers.