Abstract: The existing unsupervised discriminant projection(UDP)algorithm only utilizes information out of the null space of local scatter matrix,which leads to the loss of information in the null space.In order to utilize information in and out of the null space of local scatter matrix simultaneously,a complete unsupervised discriminant projection(CUDP)algorithm is proposed.In the null space of local scatter matrix,effective features are extracted by maximizing nonlocal scatter.Out of the null space of local scatter matrix,effective features are extracted by maximizing nonlocal scatter and by minimizing local scatter simultaneously.At last,the CUDP features are obtained by combining these two kinds of features.The results of face recognition experiments on ORL and FERET databases and face expression recognition experiment on CMU and Yale databases demonstrate the effectiveness of our proposed CUDP.