<p>Great advances have been achieved in the study of entanglement characteristics. However, even for <i>N</i>-qubit systems, the problem of the entanglement criterion has not been well solved. In this paper, starting from the local hidden variable theory, and using the state decomposition and higher-order singular value decomposition, we propose a sufficient separable criterion for <i>N</i>-qubit systems, which serves as a full separable system criterion. As examples, we apply our method to study multi-qubit states with white noise. Using this method, we can obtain the decomposition of separable pure states. For the two-qubit case, we provide an entanglement monotone which gives similar results to concurrence up to a factor. Our results pave the way for solving the entanglement-separability criterion from a new perspective.</p>