  We analyse a little known aspect of the Klein paradox. A Klein-Gordon boson
appears to be able to cross a supercritical rectangular barrier without being
reflected, while spending there a negative amount of time. The transmission
mechanism is demonstrably acausal, yet an attempt to construct the
corresponding causal solution of the Klein-Gordon equation fails. We relate the
causal solution to a divergent multiple-reflections series, and show that the
problem is remedied for a smooth barrier, where pair production at the energy
equal to a half of the barrier's height is enhanced yet remains finite.
