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We give a new separability criterion, a necessary condition for separabilityof $N$-partite quantum states. The criterion is based on the Blochrepresentation of a $N$-partite quantum state and makes use of multilinearalgebra, in particular, the matrization of tensors. Our criterion applies to{\it arbitrary} $N$-partite quantum states in$\mathcal{H}=\mathcal{H}^{d_1}\otimes \mathcal{H}^{d_2} \otimes ... \otimes\mathcal{H}^{d_N}.$ The criterion can test whether a $N$-partite state isentangled and can be applied to different partitions of the $N$-partite system.We provide examples that show the ability of this criterion to detectentanglement. We show that this criterion can detect bound entangled states. Weprove a sufficiency condition for separability of a 3-partite state,straightforwardly generalizable to the case $N > 3,$ under certain condition.We also give a necessary and sufficient condition for separability of a classof $N$-qubit states which includes $N$-qubit PPT states.

Separability Criterion for multipartite quantum states based on the Bloch representation of density matrices