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Cancer diagnosis is one of the most important emerging clinical applications of gene expression microarray technology. In this paper, the global k-means algorithm was adopted to cluster genes in training samples sets. The gene with largest Dudoit ratio in each cluster was picked as a characteristic gene. A multiclass support vector machine (SVM) was developed as a classifier for the prediction of cancer types. With a test on LC197 data set and TC168 data set, the method in this paper not only achieved better performances than One-vs-One SVM and One-vs-Rest SVM, but also outperformed k-nearest neighbors and artificial neural network. These results render this method a viable alternative to other classification methods for cancer diagnosis.