  We first present a generalized criterion for maximally entangled states of 2,
3, 4, 5, 6, 8 and in theory to arbitrary-number qubits. By this criterion, some
known highly entangled multi-qubit states are examined and a new genuine
eight-qubit maximally entangle state is obtained. For the 4, 7 and 8 qubits
system in which no maximally multi-qubit entangled states (MMES) is thought to
exist before, we find that the proved and most suspected MMESes, are not
completely mixed in subsystem with a critical-number qubits, below which the
subsystems are all completely mixed. We believe that the new criterion and MMES
can play important role in quantum information technology, such as the
teleportation and dense coding.
