In　2005,　Sui　et　al.　proposed　two　separable　and　anonymous　identity-based　key　issuing　schemes,　but　the　impersonation　attack　is　proposed　to　show　that　Sui　et　al.＇s　second　protocol　is　not　free　from　the　key-escrow　problem.　In　order　to　solve　such　problem,　Feng　Cao　et　al.　proposed　an　improved　scheme　in　2006.　However,　in　the　paper,　we　find　that　Feng　Cao　et　al.＇s　scheme　is　still　vulnerable　to　the　impersonation　attack.　According,　the　current　paper　first　shows　the　weakness　of　Feng　Cao　et　al＇s　improved　scheme,　and　then　proposes　our　improvement　which　reaches　the　goal　of　avoiding　key　escrow　problem　and　enhances　efficiency.　©　2008　IEEE.