Mining frequent itemsets utilizing multiple minimum supports is an essential generalization of the association rule mining problem. Instead of setting a single minimum support for all items, users are allowed to specify different minimum support values to different items. In real applications, using single minimum item support is inadequate since it does not reflect the nature of each item. If single minimum support is set to low, a large number of association rules are generated. On the other hand, if it is set to high, important rules may be lost. In this paper, we proposed an algorithm named Relative Multiple Supports Apriori (RMSApriori) to solve the problem of single multiple support. It is compared with the original Apriori and various experiments are conducted using real datasets. Different values of single minimum support were applied on each dataset for comparison and rules involving frequent and rare items were found. However, the minimum support value has to be set to low resulting in an increase of processing time and space. Experimental results reveal that RMSApriori outperforms Apriori in terms of execution time and memory usage considering the generation of rules not only for frequent items but also for significant rare items.