Selection of significant genes via expression patterns is an important problem in microarray data processing. In this article, we propose and study a new method for selecting relevant genes obtained by spectral biclustering and based on similarity between genes and eigenvectors. The proposed algorithm can select a much smaller gene subset to make accurate predictions. The unsupervised gene selection method suggested in This work is demonstrated on two microarray cancer data sets, i.e., the lymphoma and the liver cancer data sets. In both examples, our method is able to identify two-gene combinations which can lead to prediction with very high accuracy.