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Selective classifiers can effectively improve the accuracy and efficiency of classification by deleting irrelevant or redundant attributes of a data set. Though many selective classifiers have been proposed, most of them deal with complete data. Yet actual data sets are often incomplete and have many redundant or irrelevant attributes. So constructing selective classifiers for incomplete data is important. In this paper a hybrid selective classifier for incomplete data, denoted as CBSD, is presented. The proposed algorithm needs no assumption about data sets that are necessary for previous methods of processing incomplete data in classification. Experiments results on twelve benchmark incomplete data sets show that CBSD can effectively improve the accuracy and efficiency of classification while enormously reducing the number of attributes.