Took the derivative and e-derivative of Boolean function as a tool

analyzed the inner structure of balanced H-Boolean functions

clearly obtained the conclusion that the second-order correlation-immune balanced H-Boolean function is not existent

solved the problem that whether there was a second-order correlation-immune balanced H-Boolean function which has not yet proper result.From the rationality of logic and theory

defined the necessity of discussing the generalized correlation-immune of balanced H-Boolean function for the security of cryptosystem.And through the analysis of generalized correlation-immunity and correlation-measure of balanced H-Boolean function

de-rived the algorithms which reduced the balanced H-Boolean function correlation-measure

and while increased the order of correlation-measure.