A　scheme　is　proposed　for　the　generation　of　W　entangled　states　for　several　atoms　trapped　in　a　cavity　by　detecting　photon　decay.　The　scheme　works　in　the　regime,　where　the　cavity　decay　rate　is　larger　than　the　atom-cavity　coupling　strength.　Thus,　the　requirement　for　the　quality　factor　of　the　cavity　is　greatly　loosened,　which　is　of　importance　in　View　of　experiment.　Another　advantage　of　this　scheme　is　that　the　atoms　are　always　populated　in　two　ground　states　coupled　by　Raman　transitions,　thus　the　spontaneous　emission　can　also　be　suppressed.