Can a particle moves zigzag in time?

Amplitudes of quantum transitions containing time zigzags are considered. The discussion is carried out in the framework of the Minkowski metric and standard quantum mechanics without adding new postulates. It is shown that the wave function is singular at the instant of the time zigzag. Nevertheless, we argue that time zigzags are not suppressed at the quantum level, but their contribution to the amplitude is zero. The result is valid for a single particle and a non-interacting scalar field.