Dempster-Shafer evidence theory is very important in the fields of information fusion and decision making. However, it always brings high computational cost when the frames of discernments to deal with become large. To reduce the heavy computational load involved in many rules of combinations, the approximation of a general belief function is needed. In this paper we present a new general principle for uncertainty reduction based on hierarchical proportional redistribution (HPR) method which allows to approximate any general basic belief assignment (bba) at a given level of non-specificity, up to the ultimate level 1 corresponding to a Bayesian bba. The level of non-specificity can be adjusted by the users. Some experiments are provided to illustrate our proposed HPR method.