Coalition　formation　is　a　key　topic　in　multiagent　systems.　One　may　prefer　a　coalition　structure　that　maximizes　the　sum　of　the　values　of　the　coalitions,　but　often　the　number　of　coalition　structures　is　too　large　to　allow　exhaustive　search　for　the　optimal　one.　But　then,　can　the　coalition　structure　found　via　a　partial　search　be　guaranteed　to　be　within　a　bound　from　optimum?　Sandholm　et　al.　showed　that　it　suffices　to　search　the　lowest　two　levels　of　the　coalition　structure　graph　in　order　to　establish　a　worst　case　bound　K(n).　Dang　et　al.　presented　an　algorithm　that　takes　a　step　further　to　search　those　coalition　structures　whose　biggest　coalition＇s　cardinality　is　greater　than　or　equal　to　⌈n(k　-　1)/(k　+　1)⌉,　which　is　the　best　result　known　so　far.　Against　this　background,　this　paper　reports　on　a　novel　anytime　algorithm　based　on　cardinality　structure　that　only　have　to　take　a　step　further　to　search　those　coalition　structures　whose　cardinality　structure　is　in　the　CCS(n,　b).　Consequently,　the　algorithm　reported　in　this　paper　is　obviously　better　than　that　of　Sandholm　et　al.　(up　to　10　35　times　faster　when　n=100,　K=2)　and　Dang　et　al　(up　to　10　18　times　faster　when　n=100,　K=3).　©　2007　IFAAMAS.