The　traditional　threshold　signature　scheme　is　a　combination　of　the　digital　signature　scheme　and　the　secret　sharing　scheme.　Any　group　of　t　(threshold　value)　or　more　players　can　reconstruct　the　secret　together　but　no　group　of　fewer　than　t　players　can　in　secret　sharing　scheme.　Because　of　this　property　of　secret　sharing　scheme,　the　current　threshold　signature　scheme　has　a　natural　weakness　in　the　anti-collusion　attack.　A　new　threshold　signature　scheme　based　on　the　factorial　decompose　theorem　is　designed　successfully　without　the　secret　sharing　scheme　in　order　to　get　the　ability　of　anti-collusion　attacks.　It　not　only　has　the　property　of　group　signature　and　threshold　signature,　but　also　has　some　good　features　including　traceability,　robustness　and　resisting　forgery　attacks.