An　alternative　scheme　is　proposed　for　engineering　three-dimensional　maximally　entangled　states　for　two　modes　of　a　superconducting　microwave　cavity.　In　this　scheme,　an　appropriately　prepared　four-level　atom　is　sent　through　a　bimodal　cavity.　During　its　passing　through　the　cavity,　the　atom　is　coupled　resonantly　with　two　cavity　modes　simultaneously　and　addressed　by　a　classical　microwave　pulse　tuned　to　the　required　transition.　Then　the　atomic　states　are　detected　to　collapse　two　modes　onto　a　three-dimensional　maximally　entangled　state.　The　scheme　is　different　from　the　previous　one　in　which　two　nonlocal　cavities　are　used.　A　comparison　between　them　is　also　made.　©　2007　Chin.　Phys.　Soc.　and　IOP　Publishing　Ltd.