Latent Semantic Indexing (LSI) is a successful technology in information retrieval (IR) which attempts to explore the latent semantics implied by a query or a document through representing them in a dimension-reduced space. However, LSI is not optimal for document categorization tasks because it aims to find the most representative features for document representation rather than the most discriminative ones. In this paper, we propose Supervised LSI (SLSI) which selects the most discriminative basis vectors using the training data iteratively. The extracted vectors are then used to project the documents into a reduced dimensional space for better classification. Experimental evaluations show that the SLSI approach leads to dramatic dimension reduction while achieving good classification results.