Intertransaction association rule mining is used to discover patterns between different transactions. It breaks the scope of association rule mining on the same transaction. Currently the FITI algorithm is the state of the art in intertransaction association rule mining. However, the FTTI introduces many unneeded combinations of items because the set of extended items is much larger than the set of items. Thus, we propose an alternative approach of granule based intertransaction association rule mining, where a granule is a group of transactions that meet a certain constraint. The experimental results show that this approach is promising in real-world industry.