Can one ever prove that neutrinos are Dirac particles?

According to the “Black Box” theorem the experimental confirmation of neutrinoless double beta decay (0ν2β) would imply that at least one of the neutrinos is a Majorana particle. However, a null 0ν2β signal cannot decide the nature of neutrinos, as it can be suppressed even for Majorana neutrinos. In this letter we argue that if the null 0ν2β decay signal is accompanied by a 0ν4β quadruple beta decay signal, then at least one neutrino should be a Dirac particle. This argument holds irrespective of the underlying processes leading to such decays.