  We show that, for Majorana neutrinos propagating in a constant magnetic
field, the flavour survival probabilities for left-handed neutrinos is the same
as for right-handed neutrinos, i.e., $P^M (\nu_{\alpha L}\to\nu_{\alpha L}) =
  P^M (\nu_{\alpha R}\to\nu_{\alpha R})$, where $\alpha = e, \mu, \tau$,
whereas in the Dirac case the corresponding probabilities $P^D (\nu_{\alpha
L}\to\nu_{\alpha L})$ and $P^D (\bar\nu_{\alpha R}\to\bar\nu_{\alpha R})$ are
in general different. This might lead to a novel way to search for the nature
of neutrinos. We also discuss how this relation for Majorana neutrinos gets
modified when the magnetic field is not constant. However, if matter effects
become important the relation does not hold anymore.
