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In this paper, we propose a new algorithm called Orthogonal Neighborhood Preserving Embedding (ONPE) for face recognition. ONPE can preserve local geometry information and is based on the local linearity assumption that each data point and its k nearest neighbors lie on a linear manifold locally embedded in the image space. ONPE is based on Neighborhood Preserving Embedding (NPE), but overcomes the metric distortion problem of NPE, while metric distortion usually leads to performance degradation. Besides, we propose a classification method (ONPC) based on the ONPE, which use local label propagation method in the reduced space for face recognition. ONPC is based on the natural assumption that the local neighborhood information is also preserved in reduced space, and the label of a data point can be obtained in the reduced space by the labels of its neighbors. Experimental results on two face databases demonstrate the effectiveness of our proposed method.