In　this　paper　a　scheme　is　proposed　for　the　purification　of　entangled　states　for　two　atoms　trapped　in　two　distant　cavities　via　cavity　decay.　In　the　scheme,　the　atoms　have　no　probability　of　being　populated　in　the　excited　state　and　thus　the　atomic　spontaneous　emission　is　suppressed.　This　scheme　is　valid　no　matter　when　the　cavity　decay　rate　is　larger　or　smaller　than　the　effective　atom-cavity　coupling　strength.　The　fidelity　of　the　final　state　is　not　affected　by　the　imperfection　of　the　photodetectors.　©　2008　Chin.　Phys.　Soc.　and　IOP　Publishing　Ltd.