A study has been made on the essence of optimal set of uncorrelated discriminant vectors in this paper. A whitening transform has been constructed on the basis of the eigen decomposition of population scatter matrix, which makes the population scatter matrix an identity matrix in the transformed sample space. Thus, the optimal discriminant vectors solved by conventional LDA methods are statistical uncorrelated. The research indicates that the essence of the statistical uncorrelated discriminant transform is the whitening transform plus conventional linear discriminant transform. The distinguished characteristic of the proposed method is that the obtained optimal discriminant vectors are orthogonal and statistical uncorrelated. The proposed method suits for all the problems of algebraic feature extraction. The numerical experiments on facial database of ORL show the effectiveness of the proposed method.