Intention,　a　crucial　part　of　the　mental　states　of　an　agent,　plays　an　important　role　in　determining　the　behaviors　of　the　rational　agent.　In　order　to　eliminate　the　flaws　with　existing　logic　of　intention　and　establish　a　suitable　semantic　representation　for　intention,　this　paper　addresses　the　requests　for　intention　semantics　on　formal　frameworks　of　rational　agents,　points　out　the　problems　with　existing　logic　of　intention,　introduces　a　novel　possible　world　semantics　for　intention,　called　the　improved　twin-subset　semantics,　which　was　developed　by　us　recently　based　on　the　previous　work　about　the　true-false　subset　semantics,　and　presents　its　application　in　the　formalization　of　intention　for　agent.　It　is　also　proved　that　some　desired　properties　could　be　obtained　through　some　restrictions　to　the　algebraic　structure　of　the　models.　In　the　two-value　logic,　the　false　value　is　as　important　as　the　true　value.　Of　course,　to　one　proposition,　once　the　true　values　are　described　in　some　possible　worlds,　the　false　values　are　just　the　rest.　However,　to　a　set　of　propositions　(the　agent　intents　to　do),　descriptions　to　the　false　values　are　as　important　as　descriptions　to　the　true　values.　The　representation　of　intention　should　describe　a　set　of　propositions　(the　propositions　agent　intents　to　achieve),　but　in　the　possible　world　semantics　of　classical　normal　modal　operator,　it　merely　pays　attention　to　the　true-value,　which　is　denoted　as　RI(w),　and　can　be　considered　as　single-subset　semantics.　In　the　improved　twin-subset　semantics,　the　false-value　is　considered　as　important　as　the　true-value,　and　RIT(w)　is　used　to　describe　the　true,　while　RIF(w)　the　false.　Thus　this　method　can　describe　modal　operator　in　two-value　logic　completely.　In　addition,　the　possible　world　semantics　of　the　classical　normal　modal　operator　can　be　regarded　as　the　degradation　of　the　improved　twin-subset　semantics　when　RIF(w)　=　∅　It　not　only　avoids　the　logical　omniscience　problem　and　other　related　problems　(such　as　side-effect　problem,　and　etc)　but　also　overcomes　the　shortcomings　of　the　true-false　subset　semantics　and　twin-subset　semantics.　Compared　with　Konolige　and　Pollack＇s　model　of　intention,　this　model　not　only　is　simpler　and　more　natural,　but　also　satisfies　the　K-axiom　and　the　Joint　Consistency.　Actually,　the　improved　twin-subset　semantics　provides　a　new　method　for　semantic　representation　of　non-normal　modal　operator　and　can　be　applied　to　establish　a　new　proper　agent＇s　logic　system.