Word classification is still an open issue for the linguistic research of Chinese.A fixed-point theory of word classification is proposed in this paper. According to our result,the Distributed Analysis (DA) method for word classification can be used in a process of iteration, so that the "logical circle" critique on DA method does not hold. The ideal classification, i. e., the maximal fixed-point, is computable in the limit. This paper therefore cleared out the misunderstandings on DA method among linguists, and proved the distribution criterion to be scientific.