Abstract: In this study, we first give a survey of the Siegenthaler’s constructions and the general Carlet’s construction of resilient functions, permitting to obtain resilient functions achieving the best possible trade-offs between resiliency order, algebraic degree and nonlinearity. Then, we introduce and we study a new secondary construction of resilient functions based on the principal of the siegenthaler’s construction. This construction permitted to increase the algebraic immunity, algebraic degree and define many more resilient functions where the degree, algebraic immunity, resiliency and nonlinearity achieving are high. Thus, permits to obtain resilient functions achieving the best possible trade-offs between resiliency order, algebraic degree and nonlinearity (that is, achieving Siegenthaler’s and Sarkar, al.’s bounds). We conclude the paper by generalizing our construction to plateaued functions.