Abstract: As a novel definition, E-derivative was introduced to study problems that are extremely difficult to handle in the cryptographic system. By using the way of combining derivative with E-derivative and correlation-immunity of H-Boolean functions, the distribution structure of balanced H-Boolean functions were deeply analyzed, and some important results on how to determine whether or not a H-Boolean function has correlation-immunity with the relatively simplified method of distinguishing different structure were also obtained, which are going to play important roles in the field of cryptology and future worldwide applications. Beyond that, the problem of the most higher-order correlation-immunity of H-Boolean function which is also one of the most difficult unsolved problems in cryptology was solved successfully to improve the anti-attack ability of cryptosystem and ensured the secure transmission of secret information on the network effectively .