<p>Sequential rule mining remains an important research topic in data mining. Discovering conditioned events in large databases can provide beneficial insights. However, periodic intra-sequential mining has also emerged as an interesting topic, describing patterns that are simultaneously periodic within sequences across different sequences. These patterns have been proven especially useful in sales and marketing, aiding in targeting a group of customers based on their common periodic behavior. Motivated by previous works, we propose a new mining task to discover periodic sequential rules that appear in multiple sequences. The goal is to find causal temporal relationships in periodic intra-sequential patterns, producing more meaningful patterns while retaining the significance of the information they provide. We also emphasize that the periodicity constraint was not introduced in partially-ordered sequential and intra-sequential rules beforehand. In this paper, we propose the periodic intra-sequential RuleGrowth (PISRuleGrowth) algorithm, which is based on the pattern-growth approach and uses a map structure to remain efficient even on large databases. Extensive experiments on real datasets confirmed that the algorithm outperforms the existing algorithms in terms of speed and memory usage.</p>