Mining for association rules between items in a large database of sales transaction has been described as an important data mining problem. The mining of association rules can be mapped into the problem of discovering large itemsets. In this paper we present an efficient algorithm for mining association rules by minimizing the total numbers of candidate 2-itemset, │C$_2$│. More the total numbers of candidate 2-itemset, less the time of executing the algorithm for mining association rules. The total performance of algorithm depends on the time of finding large 2-itemsets. Hence, minimizing the total numbers of candidate 2-itemset is very important. We have performed extensive experiments and compared the performance of our algorithm with the DHP algorithm, the best existing algorithm.