We experimentally demonstrate observation of highly pure four-photon GHZ entanglement producedby parametric down-conversion and a projective measurement. At the same time this also demonstrates
teleportation of entanglement with very high purity. Not only does the achieved high visibility enablevarious novel tests of quantum nonlocality, it also opens the possibility to experimentally investigatevarious quantum computation and communication schemes with linear optics. Our technique can, inprinciple, be used to produce entanglement of arbitrarily high order or, equivalently, teleportation and entanglement swapping over multiple stages.