  Genuine multipartite entanglement is of great importance in quantum
information, especially from the experimental point of view. Nevertheless, it
is difficult to construct genuine multipartite entangled states systematically,
because the genuine multipartite entanglement is unruly. We propose another
product based on the Kronecker product in this paper. The Kronecker product is
a common product in quantum information with good physical interpretation. We
mainly investigate whether the proposed product of two genuine multipartite
entangled states is still a genuine entangled one. We understand the
entanglement of the proposed product better by characterizing the entanglement
of the Kronecker product. Then we show the proposed product is a genuine
multipartite entangled state in two cases. The results provide a systematical
method to construct genuine multipartite entangled states of more parties.
