  The recently discovered so-called BSW effect consists in the unbound growth
of the energy E_{c.m.} in the centre of mass frame of two colliding particles
near the black hole horizon. We consider a new type of the corresponding
scenario when one of two particles ("critical") remains at rest near the
horizon of the charged near-extremal black hole due to balance between the
attractive and repulsion forces. The other one hits it with a speed close to
that of light. This scenario shows in a most pronounced way the kinematic
nature of the BSW effect. In the extremal limit, one would gain formally
infinite E_{c.m.} but this does not happen since it would have require the
critical massive particle to remain at rest on the null horizon surface that is
impossible. We also discuss the BSW effect in the metric of the extremal
Reissner-Nordstr\"om black hole when the critical particle remains at rest near
the horizon.
