  In entanglement theory, there are different methods to consider one state
being more entangled than another. The "maximally" entangled states in a
multipartite system can be defined from an axiomatic perspective. According to
different criteria for selection, there are many specific types of quantum
maximally entangled states, such as absolutely maximally entangled state,
planar maximally entangled state and so on. In this paper we propose a new type
of maximally entangled states, the planar two-region multipartite maximally
entangled state. The requirement condition of this maximally entangled state is
weak than that of the absolutely maximally entangled state and different from
that of the planar maximally entangled state. We show that there are the
two-region four-partite maximally entangled states in 4-qubit and 7-qubit
planar systems, although there is no absolutely maximally entangled state in
these systems. It is proved that there are the planar two-region four-partite
maximally entangled states in both even particle quantum systems and odd
particle quantum systems. Additionally, based on some planar two-region
four-partite maximally entangled states, the new planar two-region four-partite
maximally entangled states are generated. We also provide some important
examples of the planar two-region multi-partite maximally entangled states.
