We　consider　an　open　quantum　system　consisting　of　four　atoms　which　are　placed　in　a　damped　cavity.　Through　a　dissipative　dynamics　process,　a　W　state　can　be　converted　into　a　Greenberger-Horne-Zeilinger　state　with　deterministic　probability.　In　addition,　the　interaction　time　need　not　be　controlled　strictly　in　the　dynamics　process.　The　protocol　may　open　up　a　promising　perspective　for　quantum　state　conversion　between　different　classes　of　entanglement　and　cavity　quantum　electrodynamics　systems.