Frequent pattern mining is the fundamental and most dominant research area in data mining. Maximal frequent patterns are one of the compact representations of frequent itemsets. There is more number of algorithms to find maximal frequent patterns that are suitable for mining transactional databases. Users not only interested in occurrence frequency but may be interested on frequent patterns that occur at regular intervals. A frequent pattern is regular-frequent, if it occurs at less than or equal to user given maximum regularity threshold. Occurrence behaviour (regularity) of a pattern may be considered as important criteria along with occurrence frequency. There is no suitable algorithm to mine maximal regular-frequent patterns retrieving at once in transactional databases also satisfies downward closure property. Thus we are introducing a new single-pass algorithm called MaRFI (Maximal Regular Frequent Itemset) which mines maximal regular-frequent patterns in transactional databases using pair of transaction-ids instead of using item-ids. Our experimental results show that our algorithm is efficient in finding maximal regular-frequent patterns.