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Lighting condition is an important factor in face analysis and synthesis, which has received extensive study in both computer vision and computer graphics. Motivated by the work on multilinear model, we propose a learning-based algorithm for relighting based on tensor framework, which explicitly accounts for the interaction of the identity factor and the lighting factor. The major contribution of our work is that we develop a novel algorithm based on a two-stage decomposition scheme to simultaneously and robustly solve for the identity parameter and the lighting parameter which are both unknown. Equipped with the decomposition algorithm, the capability of the tensor model is significantly extended. Experiment results illustrate the effectiveness of our algorithm.