  As is well-known, there exist totally three CP-violating phases in the
leptonic sector if three ordinary neutrinos are massive Majorana particles. In
this short note, we raise the question whether the number of sufficient and
necessary conditions for CP conservation in the leptonic sector with massive
Majorana neutrinos is three or four. An intuitive answer to this question would
be three, which is also the total number of independent CP-violating phases.
However, we give a counter example, in which three conditions are in general
not sufficient for CP conservation. Only for all the lepton masses and mixing
angles within their experimentally allowed ranges can we demonstrate that it is
possible to find out three weak-basis invariants, which should be vanishing to
guarantee leptonic CP conservation.
