Channel　routing　in　the　2-layer　Manhattan　model　is　one　of　the　most　investigated　problems　in　VLSI　design.　Da´vid　Szeszle´r　[Szeszle´r　D.,　A　New　Algorithm　for　2-layer,　Manhattan　Channel　Routing,　Proc.　3rd　Hungarian-Japanese　Symposium　on　Discrete　Mathematics　and　Its　Applications　(2003),　179-185]　gave　a　complete　characterization　of　all　specifications　that　are　solvable　and　present　a　linear　time　algorithm　to　solve　these　specifications　with　a　width　at　most　constant　times　the　length　of　the　problem.　In　this　paper　an　efficient　graph　theoretic　algorithm　for　a　particular　2-layer　Manhattan　channel　routing　problem　has　been　presented,　we　give　a　new　polynomial　time　algorithm　to　solve　these　specifications　with　a　width　better　than　the　result　of　Da´vid　Szeszle´r.　©　2012　by　IJAMAS,　CESER　Publications.