  According to the "Black Box" theorem the experimental confirmation of
neutrinoless double beta decay ($0 \nu 2 \beta$) would imply that at least one
of the neutrinos is a Majorana particle. However, a null $0 \nu 2 \beta$ 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 $0 \nu 2 \beta$
decay signal is accompanied by a $0 \nu 4 \beta$ 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.
