  We explore all the trade-off relations of multipartite quantum discord
proposed very recently in [Phys. Rev. Lett. {124}, 110401~(2020)] and show that
the multipartite quantum discord is completely monogamous provided that it does
not increase under discard of subsystems. Here, a quantity of multipartite
quantity, with the same spirit as established in [Phys. Rev. A. {101},
032301~(2020)], is said to be completely monogamous (i) if it does not increase
under loss of subsystems and (ii) if some given combination of subsystems reach
the total amout of correlation, then all other combination of subsystems that
excluding the given subsystems do not contain such a correlation any more. In
addition, we explore all the trade-off relations for the global quantum discord
proposed in [Phys. Rev. A 84, 042109 (2011)] and show that the global quantum
discord is not completely monogamous.
