It is firmly believed that a signal of neutrinoless double beta decay can confirm the Majorana nature of neutrinos. However, we remind another possibility that a Majorana neutrino mass induced after some neutrinoless double beta decay processes can be accidentally cancelled by another Majorana neutrino mass induced before any neutrinoless double beta decay processes. This cancellation can simultaneously allow an observable neutrinoless double beta decay and a vanishing Majorana neutrino mass. In consequence, a future discovery of neutrinoless double beta decay cannot fully rule out the possibility of Dirac neutrinos. For demonstration, we simply show a realistic model with observable neutrinoless double beta decay and purely Dirac neutrinos.