A　scheme　is　proposed　for　the　generation　of　entangled　states　for　multiple　atoms　trapped　in　a　cavity　by　detecting　photon　decay.　The　scheme　is　valid　no　matter　when　the　effective　atom-cavity　coupling　strength　is　larger　than　the　cavity　decay　rate　or　not,　which　is　of　importance　in　view　of　experiment.　The　fidelity　of　entanglement　is　insensitive　to　the　inefficiency　of　the　photo-detector.　The　scheme　does　not　require　a　photon　to　be　initially　injected　into　the　cavity.　©　International　Academic　Publishers.