  The complex Langevin method is a promising approach to the complex-action
problem based on a fictitious time evolution of complexified dynamical
variables under the influence of a Gaussian noise. Although it is known to have
a restricted range of applicability, the use of gauge cooling made it
applicable to various interesting cases including finite density QCD in certain
parameter regions. In this paper, we revisit the argument for justification of
the method. In particular, we point out a subtlety in the use of time-evolved
observables, which play a crucial role in the previous argument. This requires
that the probability of the drift term should fall off exponentially or faster
at large magnitude. We argue that this is actually a necessary and sufficient
condition for the method to be justified. Using two simple examples, we show
that our condition tells us clearly whether the results obtained by the method
are trustable or not. We also discuss a new possibility for the gauge cooling,
which can reduce the magnitude of the drift term directly.
