This paper presents a new iterative algorithm for feature generation, which is approximately derived based on geometrical interpretation of the Fisher linear discriminant (FLD) analysis. In a field of pattern recognition or signal processing, the principal component analysis (PCA) is popular for data compression and feature extraction. Furthermore, iterative learning algorithms for obtaining eigenvectors in PCA have been presented in a field of pattern recognition, image analysis, and neural networks. Their effectiveness has been demonstrated in many applications. However, recently the FLD analysis has been used in many fields, especially face image analysis. The drawback of FLD is a long computational time in compression of a large-sized between-class covariance 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.