Let　(X,　Y),　(X-1,Y-1),　...　,　(X-n,　Y-n)　be　R-d　x{1,　...　,　M}　-valued　i.i.d.　random　vectors,　Z(n)　=　{(X-1,　Y-1),　...　(X-n,　Y-n)}.　(X,　Y)　is　distribution　free,　to　discriminate　Y　based　on　Z(n)　and　X　belongs　to　nonparametric　discrimination.　Based　on　kernel　stereographic　projection　density　estimator　(KSPDE),　a　new　nonparametric　discriminate　rule　is　constructed.　Under　some　weak　conditions(see　theorem　1),　the　exponential　convergence　rate　and　the　strong　consistency　of　the　conditional　probability　of　error　in　discrimination　are　obtained.