Reversibility of local transformations of multiparticle entanglement

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.