Summary: We give a simple and general explanation for the effect of unbound acceleration of particles by black holes. It is related to the fact that the scalar product of a timelike vector of the four-velocity of an ingoing particle and the lightlike horizon generator tends to zero in some special cases, so the condition of ‘motion forward in time’ is marginally satisfied. In this sense, an ingoing particle with a special relation between parameters imitates the property of infinite redshift typical of any outgoing particle near the future horizon of a black hole. We check this assertion using the Reissner-Nordström and rotating axially symmetric metrics as examples.