We present a physical scheme to teleport an unknown atomic entangled state via cavity decay. In the teleportation process, four-particle Greenberger-Horne-Zeilinger (GHZ) state is used as quantum channel, and two unknown entangled atoms and two of four atoms in the four-particle GHZ state are trapped in four leaky cavities,respectively. Based on the joint detection of the photons leak out from the four cavities, we can teleport an unknown entangled state to two other remote atoms with certain probability and high fidelity.