In this paper，the problem of the consistency of knowledge bases in their maintenance is first described，and then a framework for extended logic programming is described．where an extended logic program is equivalent to a knowledge base. In orde to check the consistency of a knowledge base，the PSS(positive support set)and the NSS (negative support set)for an inference rule in the base are constructed, and some detini-tions are given．Based on these concepts and definitions，an effective method of checking knowledge bases for the consistency in their maintenance is presented，and the related the-orems are proved．Based on this method，an algorithm，called CHIME，is implemented, and the experimental results for analyzing some knowledge bases in CHIME are shown.Some related work is also mentioned．Finally，the conclusion of this paper is given.