  We consider the transformation of multisystem entangled states by local
quantum operations and classical communication. We show that, for any
reversible transformation, the relative entropy of entanglement for two parties
must remain constant. This shows, for example, that it is not possible to
convert 2N three party GHZ states into 3N singlets, even in an asymptotic
sense. Thus there is true three-party non-locality (i.e., not all three-party
entanglement is equivalent to two-party entanglement). Our results also allow
us to make {\em quantitative} statements about concentrating multi-particle
entanglement. Finally, we show that there is true n-party entanglement for all
n.
