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Designing efficient algorithm for computing the core of decision table is a very meaningful work because the core is the foundation of constructing attribute reduction of the decision table and multi-variable decision tree. To improve the efficiency of the algorithm for computing the core based on Skowron's discernibility matrix with database technology, the new simplified decision table of the old decision table is defined. And it is proved that the core of the new simplified decision table based on positive region is the same as the core of the old one based on Skowron's discernibility matrix. Then an efficient algorithm is proposed for computing the new simplicity decision table. On this condition, an efficient algorithm for computing the core based on Skowron's disceribility matrix by using database technology is designed. At the end, an example is used to illustrate the efficiency of the new algorithm.