The problems of previous methods for constructing the core attributes by discernibility matrix are discussed and the causes of the problems are investigated. A generalized definition of reduction is proposed, and the definitions of necessary discernibility relation and unnecessary discernibility relation are presented, by which a generalized discernibility matrix is presented. With the definition of generalized reduction, an improved discernibility matrix for constructing core attributes proposed by previous researcher is compared with the the classical discernibility matrix proposed by Skowron, and it is concluded that the two matrix are in fact indiscrimination.