This paper develops an unsupervised discriminant projection (UDP) technique for feature extraction. UDP takes the local and non-local information into account, seeking to find a projection that maximizes the non-local scatter and minimizes the local scatter simultaneously. This characteristic makes UDP more intuitive and more powerful than the up-to-date method locality preserving projection (LPP, which considers the local information only) for classification tasks. The proposed method is applied to face biometrics and examined using the ORL and FERET face image databases. Our experimental results show that UDP consistently outperforms LPP, PCA, and LDA.