Abstract: A novel class of n+t-variable Boolean functions G(x,y) through adding t variables while concatenating t+1 Boolean functions (called basic function) was constructed and the Walsh spectrum and autocorrelation coefficient of G(x,y) were given. The relationship between G(x,y) and basic functions by Krawtchouk polynomial and Krawtchouk matrix was studied. Moreover, their cryptographic properties: correlation immunity, propagation and algebraic immunity were investigated. Specially, the detailed relationship between G(x,y) and basic functions when t=2 was analyzed. In additional, a novel class of multioutput Boolean functions by generalizing the method was constructed and the general Walsh spectrum of the class of multioutput Boolean functions was proposed. Correlation immunity and algebraic immunity of the class of multioutput Boolean functions were analyzed.