In many high-dimensional microarray classification problems, an important task is to identify subsets of genes that best discriminate the classes. Nevertheless, existing gene selection methods for microarray classification cannot identify which classes are discriminable by these selected genes. In this paper, we propose an improved linear discriminant analysis (LDA) method that simultaneously selects important genes and identifies the discriminable classes. Specifically, a pairwise fusion penalty for LDA was used to shrink the differences of the class centroids in pairs for each variable and fuse the centroids of indiscriminable classes altogether. The numerical results in analyzing 2 gene expression profiles demonstrate the proposed approach help improve the interpretation of important genes in microarray classification problems.