Abstract <p>Process mining methods are aimed at modelling and analysing process data generated by information systems. The processes often contain nonrecurring events that occur no more than once per case. Thus, a process model should not contain cycles with such events. If a cycle contains a nonrecurring event, we refer to it as a fake cycle. Existing process discovery algorithms produce process models with fake cycles that distort the observed behaviour of the process and reduce model precision. Fake cycles can be avoided by allowing multiple vertex instances for the same event in a process model, which breaks the cycles. In this paper, we propose a new algorithm to discover directly-follows graph process models without fake cycles. The algorithm partitions the event log into sublogs and merges the models discovered from these sublogs while preserving structural correctness. The effectiveness of the algorithm is tested on both real and synthetic event logs. The results demonstrate that the partition-merge approach produces models that preserve fitness while avoiding the introduction of fake cycles.</p>