  We find that the mixed maximally entangled states exist and prove that the
form of the mixed maximally entangled states is unique in terms of the
entanglement of formation. Moreover, even if the entanglement is quantified by
other entanglement measures, this conclusion is still proven right. This result
is a supplementary to the generally accepted fact that all maximally entangled
states are pure. These states possess important properties of the pure
maximally entangled states, for example, these states can be used as a resource
for faithful teleportation and they can be distinguished perfectly by local
operations and classical communication.
