In this paper, we propose a novel approach for facial expression decomposition - Higher-Order Singular Value Decomposition (HOSVD), a natural generalization of matrix SVD. We learn the expression subspace and person subspace from a corpus of images showing seven basic facial expressions, rather than resort to expert-coded facial expression parameters as in [3]. We propose a simultaneous face and facial expression recognition algorithm, which can classify the given image into one of the seven basic facial expression categories, and then other facial expressions of the new person can be synthesized using the learned expression subspace model. The contributions of this work lie mainly in two aspects. First, we propose a new HOSVD based approach to model the mapping between persons and expressions, used for facial expression synthesis for a new person. Second, we realize simultaneous face and facial expression recognition as a result of facial expression decomposition. Experimental results are presented that illustrate the capability of the person subspace and expression subspace in both synthesis and recognition tasks. As a quantitative measure of the quality of synthesis, we propose using Gradient Minimum Square Error (GMSE) which measures the gradient difference between the original and synthesized images.