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In this paper, we introduce the class of k-partite episodes, which are time-series patterns of the form 〈A1,..., Ak〉 for sets Ai (1 ≤ i ≤ k) of events meaning that, in an input event sequence, every event of Ai is followed by every event of Ai+1 for every 1 ≤ i k. Then, we present a backtracking algorithm KPAR and its modification KPAR2 that find all of the frequent k-partite episodes from an input event sequence without duplication. By theoretical analysis, we show that these two algorithms run in polynomial delay and polynomial space in total input size.