In this paper, we propose a new statistical learning algorithm. This study quantitatively verifies the effectiveness of its feature extraction performance for face information processing. Smple-FLDA is an algorithm based on a geometrical analysis of the Fisher linear discriminant analysis. As a high-speed feature extraction method, the present algorithm in this paper Is the improved version of Smple-FLDA. First of all, the approximated principal component analysis (learning by Simple-PCA) that uses the mean vector of each class is calculated. Next, In order to adjust within-class variance in each class to 0, the vectors in the class are removed. By this processing, it becomes high-speed feature extraction method than Smple-FLDA. The effectiveness is verified by computer simulations using face images.