  We propose a new type of polygamy inequality for multi-party quantum
entanglement. We first consider the possible amount of bipartite entanglement
distributed between a fixed party and any subset of the rest parties in a
multi-party quantum system. By using the summation of these distributed
entanglements, we provide an upper bound of the distributed entanglement
between a party and the rest in multi-party quantum systems. We then show that
this upper bound also plays as a lower bound of the usual polygamy inequality,
therefore the strong polygamy of multi-party quantum entanglement. For the case
of multi-party pure states, we further show that the strong polygamy of
entanglement implies the strong polygamy of quantum discord.
