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Time series is acknowledged as one of the most common crucial data types in our daily lives. Among the time series mining tasks, rule discovery is important to provide valuable knowledge that brings us a profound insight view of relationships between different objects through time. One challenge is that when the number of objects and their lengths increase, it easily leads to a combinatorial explosion. Therefore, we propose a temporal inter-object association rule mining algorithm, NPTR, to discover new informative temporal inter-object association rules from time series and overcome the challenge with parallelization. Another remarkable point is that NPTR defines a concurrent approach by performing the frequent pattern mining process and rule mining one simultaneously. From the experiments on real-world data, NPTR returns the rules exactly with less time and memory costs than others do. Those rules can be further utilized for other tasks such as prediction, classification, and clustering.