Neighborhood Preserving Embedding (NPE) is a linear approximate of Locally Linear Embedding with local geometry preserving property. An efficient face recognition method requires a mapping to separate within-class structure from between-class structure. But, NPE is not in the case since it is unsupervised. Hence, we improved NPE- utilizing the neighbor and class relations of face data. The proposed technique, Neighborhood Discriminant Embedding (NDE), takes into account the local neighboring and the between-class neighboring information. NDE seeks a projection in such that the projected samples of different classes are far apart. Experimental results show that NDE achieves superior results to NPE in face authentication with error reduction at least 20%.