We　propose　a　simple　scheme　for　the　generation　of　multi-atom　Greenberger-Horne-Zeilinger　(GHZ)　states.　Three　appropriately　prepared　atoms　are　sent　through　a　nonresonant　cavity　filled　with　a　coherent　field.　The　whole　system　evolves　into　an　entangled　state,　in　which　two　three-atom　maximally　entangled　states　are　correlated　with　coherent　field　states　separated　by　π　in　phase　space.　The　field　is　then　driven　by　a　classical　current　and　measured　by　an　atom,　which　collapses　the　atomic　system　onto　a　GHZ　state.　The　scheme　can　be　easily　generalized　to　prepare　n-atom　maximally　entangled　states.