In this paper, we propose a novel approach, which is called as nonnegative matrix factorization (NMF), to analyze genome wide expression data. One of NMF advantages is that it can directly process these data without normalization. Firstly, we design an optimal algorithm for NMF approach. Compared with the existing NMF algorithms, our algorithm is more stable and converges very fast. We have coded the final algorithm in highly optimized C. Secondly, we describe the use of NMF in the extraction of the characteristic patterns from genome wide expression data. Thirdly, some simulation experiments are made in order to verify the efficiency of NMF algorithm, our conclusions are that NMF can be used as a powerful tool to extract the biologically-meaningful expression patterns from genomic wide expression data.