The transitions of electrons from positive to negative energies were examined by Klein (1) and Sauter (2) who investigated the results of including a potential step function in relativistic field equations. In this paper we arrive at a possible physical significance of the Klein paradox by examining the effect of a repulsive square potential in the Klein-Gordon equation. We find that scattering resonances can occur, and that there is also the possibility of having bound states for bosons of suitable quantum numbers. The phenomenological model gives a reasonable fit to present pion-baryon data for strangeness 0 and — 1.