We propose a Tensor Decomposition based algorithm that recognizes the observed action performed by an unknown person and unknown viewpoint not included in the database. Our previous research aimed motion recognition from one single viewpoint. In this paper, we extend our approach for human motion recognition from an arbitrary viewpoint. To achieve this issue, we set tensor database which are multi-dimensional vectors with dimensions corresponding to human models, viewpoint angles, and action classes. The value of a tensor for a given combination of human silhouette model, viewpoint angle, and action class is the series of mesh feature vectors calculated each frame sequence. To recognize human motion, the actions of one of the persons in the tensor are replaced by the synthesized actions. Then, the core tensor for the replaced tensor is computed. This process is repeated for each combination of action, person, and viewpoint. For each iteration, the difference between the replaced and original core tensors is computed. The assumption that gives the minimal difference is the action recognition result. The recognition results show the validity of our proposed method, the method is experimentally compared with Nearest Neighbor rule. Our proposed method is very stable as each action was recognized with over 75% accuracy.