Abstract: Association rules mining is an important branch of data mining. Most of association rules mining algorithms make use of only one minimum support to mine items, which may be of different nature. Due to the difference in nature of items, some items may appear less frequent and yet they are very important, and setting a high minimum support may neglect those items. And setting a lower minimum support may result in combinatorial explosion. This result in what is termed as "rare item problem". To address that, many algorithm where developed based on multiple minimum item support, where each item will have its minimum support. In this research paper, a faster algorithm is designed and analyzed and compared to the widely known enhanced Apriori algorithm. An experiment has been conducted and the results showed that the new algorithm can mine out not only the association rules to meet the demands of multiple minimum supports and but also mine out the rare but potentially profitable items' association rules, and is also proved to be faster than the conventional enhanced Apriori