A rigorous solution of Schr?idinger equation of an isotonic oscillator is studied by pseudo-angular-momentum method. The effect of the parameter g in the centripetal potential barrier on the domain of effective values for formation of stationary bounded states and the effect of domain of the parameter g on the energy spectrum are discussed in detail. An appropriate and comprehensive formulation of the energy spectrum and analytic expressions of the corresponding eigenstates are presented. The different treatments in the literatures are clarified.