In this research is presented algorithm for classification of textual documents which are represented in the space of reduced dimension in respect to original bag of words representation. Algorithm is carried out in two steps: in the first step classification is conducted for documents represented in original bag of words representation, while in the second step classification is conducted for documents represented in the space of reduced dimension. Reduction of dimensionality is obtained also in two steps: in the first step documents are represented by usage of latent semantic indexing, while in the second step this representation is projected on the space of membership matrix defining a membership of documents in classes. Evaluation of algorithm is conducted on Reuters21578 collection of documents.