Coalition　formation　is　a　key　topic　in　multi-agent　systems.　To　date,　most　work　on　this　problem　has　concentrated　on　simple　characteristic　function　games.　However,　this　lacks　the　notion　of　tasks　which　makes　it　more　difficult　to　apply　it　in　many　applications.　Dang　et　showed　that　this　problem　was　NP-hard　and　that　the　minimum　number　of　coalition　structures　that　need　to　be　searched　through　in　order　to　establish　a　solution　within　a　bound　from　the　optimal　was　(2　m+n-1-1).　Then　Dang　et　presented　an　algorithm　that　takes　a　step　further　to　search　those　task-based　coalition　structures　whose　biggest　task-based　coalition＇s　cardinality　is　greater　than　or　equal　to　⌈n(K　-　1)　/(K　+　1)　⌉　in　order　to　attain　the　bound　K,　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　task-based　coalition　structures　whose　cardinality　structure　is　in　the　CTCS(n,　m,　K*).　Finally　via　contrast　experiment,　the　algorithm　reported　in　this　paper　is　obviously　better　than　that　of　Dang　et　al.　(up　to　10　19　times　faster　when　n=60,m=40,　K=3).　©　Springer-Verlag　Berlin　Heidelberg　2009.