The first aim of this paper is to discuss the complexity of a class of cryptographically goodBoolean function-plateaued functions. Based on properties of the Walsh transform of Boolean functions, we showthat plateaued functions still keep high nonlinear after being decomposed. We then prove that the normality ofany given plateaued function has strong relationship withthe normality of its component functions. At last, a secondary construction of m-variable plateaued functions fromm-variable plateaued functions was presented. We demonstrate that a class of functions with given cryptographicproperty can be constructed, and generally the constructedfunction does not belong to Maiorana-McFarland's class.