Coalition　formation　is　a　key　topic　in　multi-agent　systems.　However,　finding　the　optimal　coalition　structure　is　NP-complete.　Sandholm　et　al.　show　that　it　is　necessary　and　sufficient　to　search　the　lowest　two　levels　of　the　coalition　structure　graph　in　order　to　establish　a　worst-case　bound　k.　How　to　do　a　further　search　after　the　lowest　two　levels　of　the　coalition　structure　graph　is　a　problem　which　hasn＇t　been　resolved　for　a　long　time.　Dang　et　al.　have　presented　an　algorithm:　for　the　odd　bound　k3,　those　coalition　structures　are　further　searched　whose　biggest　coalition＇s　cardinality　is　not　less　than　⌈n(k-1)/(k+1)⌉,　which　is　the　first　algorithm　known　whose　searching　unit　is　not　level　and　it　is　obviously　faster　than　that　of　Sandholm　et　al　for　the　smaller　bound.　The　authors　analyze　the　relations　among　coalition　structures　deeply　and　present　an　algorithm　that　only　needs　to　search　those　coalition　structures　whose　biggest　coalition＇s　cardinality　is　equal　to　⌈n(k-1)/(k+1)⌉　to　decrease　largely　the　number　of　coalition　structures　needed　to　be　searched.　Moreover,　the　algorithm　is　improved　to　search　skillfully　those　corresponding　levels　whose　coalition　structures　are　fewer　than　some　of　those　coalition　structures　whose　biggest　coalition＇s　cardinality　is　equal　to　⌈n(k-1)/(k+1)⌉,　therefore　decreasing　further　the　number　of　coalition　structures　needed　to　be　searched　and　improving　largely　the　work　of　Sandholm　et　al.　and　Dang　et　al.