  It has been shown by Ba\~{n}ados, Silk and West (BSW) that the center of mass
energy (E_cm) of test particles starting from rest at infinity and colliding
near the horizon of a Schwarzschild black hole is always finite. In this
communication, we extent the BSW scenario and study two particles with
different energies colliding near the horizon of a static spherically symmetric
black hole. Surprisingly, we find that even for the static spherically
symmetric (i.e., Schwarzschild like) black holes it is possible to obtain an
arbitrarily high E cm from the two test particles colliding near the horizon of
a black hole, if one fine-tunes the parameters of geodesic motion.
