A normal mixture model with which dependence between classes is incorporated is proposed in order to detect differentially expressed genes. Gene clustering approaches suffer from the high dimensional column of microarray expression data matrix which leads to the over-fit problem. Various methods are proposed to solve the problem. In this paper, use of simple averaging data within each class is proposed to overcome the various problems due to high dimensionality when the normal mixture model is fitted. Some experiments through simulated data set and real data set show its availability in actuality.