Linear discriminant analysis (LDA) is applied to broad areas, e.g. image recognition. However, successive learning algorithms for LDA are not sufficiently studied while they have been well established for principal component analysis (PCA).Recently, a successive leaning algorithm, which does not need N ? N matrices, has been proposed for LDA, where N is the dimension of data. In the present paper, an improvement of this algorithm is examined based on Sanger's idea. By the original algorithm, we can obtain only the subspace, which is spanned by major eigenvectors. On the other hand, we can obtain major eigenvectors themselves by the improved algorithm.