In this paper, a fuzzy hyperresolution principle called CFHR. Compensatory Fuzzy Hyperresolution, with positive compensation facility is proposed. Usually hyperresolution has several terms of conditon parts. Theser terms have to be connected by the an connective. If the main/max operator to be used the and operation, there is some dependency problem of the min/max operator. So , we propose a compensatory operator EGM and applied it to the CFHR, We show the CFHR does more meaningful reasoning than existing method. We also prove the completeness of CFHR.