In this paper the concept of partially perfect nonlinear (PPN) function is introduced as an extension of binary partially Bent function and is used to construct a new class of Boolean functions with good cryptographic properties. The construction is a composition of a PPN function and a Boolean function. The nonlinearity, correlation immunity, propagation criterion, and other cryptographic properties of the constructed functions are analyzed. In particular, new plateaued functions can be obtained by the proposed method and the construction of Khoo and Gong in [1] is improved.