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It has been shown by Bañados, 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 short note, we extent the BSW scenario and study two particles with different energies colliding near the horizon of a static spherically symmetric black hole. Interestingly, we find that even for the static spherically symmetric (ie, Schwarzschild like) black holes it is possible to obtain an arbitrarily high E cm from the two test particles colliding near but outside of the horizon of a black hole, if one fine-tunes the parameters of geodesic motion.