This paper analyzes that the main difficulty in reasoning with general terminological axioms is that the membership degrees of fuzzy interpretations are not discrete, but continous in [0,1]. To remove this obstacle difficulty, this paper proposes a discretization method of fuzzy interpretation to translate membership degrees into discrete values in a finite set. Based on this discretization, it gives a discrete Tableau reasoning technique for FALCN reasoning problems with general terminological axioms, which consists of the definition of discrete Tableaus, a construction algorithm for discrete Tableaus and the proof of soundness, completeness and complexity of this algorithm.