By using a well known result in combinatorics, named K(o)nig Lemma, this paper generalized the method of constructing measure by repeated subdivision, which was a basic tool for fractal geometry. A more general method was presented to construct measure, which was an essential improvement to the existing result. The proof employed a skill similar to that for K(o)nig Lemma, which helped to avoid using the compactness in Euclidean space. Two conditions of the existing method were found not necessary.