By connecting a small resilient functions with a vector Boolean functions with very high nonlinearity

this paper shown that there existed an（n

m

t） resilient function whose nonlinearity was 2n-1-2n-l/2-1+2l/2·nlmax（n-l

m

t）.Therefore

we improved Kurosawa’s nonlinearity 2n-1-2n-l/2-1 under the same conditions.Particularly

we constructed two concrete resilient functions using the same method

and obtained two different nonlinearities.At most of the cases

the nonlinearity of the constructed resilient function is the best compared with previous construction methods.