This paper presents a new algorithm for feature generation, which is approximately derived based on geometrical interpretation of the Fisher linear discriminant analysis. In a field of pattern recognition or signal processing, the principal component analysis (PCA) is often used for data compression and feature extraction. Furthermore, iterative learning algorithms for obtaining eigen-vectors have been presented in pattern recognition and image analysis. Their effectiveness has been demonstrated on computational time and pattern recognition accuracy in many applications. However, recently the Fisher linear discriminant (FLD) analysis has been used in such a field, especially face image analysis. The drawback of FLD is a long computational time in compression of large-sized between-class and within-class covariance matrices. Usually FLD has to carry out minimization of a within-class variance. However in this case the inverse matrix of the within-class covariance matrix cannot be obtained, since data dimension is higher than the number of data and then it includes many zero eigenvalues. In order to overcome this difficulty, a new iterative feature generation method, a simple FLD is introduced and its effectiveness is demonstrated.