An algorithm based on Bucket Sort for computing U/C is proposed, whose complexity is cut down to O(|C||U|). And a method is designed to estimate whether the change of positive region or not, which doesn’t compute positive region. A fast attribute reduction algorithm based on U/C is introduced. The reduction strategy of the algorithm is to compute relative core. If in some iteration the algorithm can not find such cores, it will eliminate one condition attribute preparing for finding relative core in the next iteration. The time complexity of the algorithm in the worst case is analyzed and its temporal complexity is O(|C|²|U/C|).