Inthispaper,wepresentanecessaryandsufficientconditionthattheperturbedmonomialmappingisergodiconasphereSp^-1(1),whichisinacombinationwithAnashin'searlierresultsabouttheperturbedmonomialergodicmappingsonasphereSp^-r(1),r>1,completelysolveaproblemposedbyA.Khrennikovabouttheergodicityofaperturbedmonomialmappingonasphere.