The quasi-relativistic harmonic oscillator bound states constructed by Znojil (1996 J. Phys. A: Math. Gen. 29 2905) are investigated via a new methodical proposal. Compared with those obtained by an anonymous referee (from a direct numerical integration method) of Znojil's paper, our results appear to be more favourable than those obtained by Znojil via quasi-perturbative, variational, Hill-determinant and Riccati-Padé methods. Bound states with larger angular momenta, l, are also constructed.