  In this paper we make re-analysis of a self-similarity based model of the
proton structure function at small \textit{x} pursued in recent years. The
additional assumption is that it should be singularity free in the entire
kinematic range $0<\textit{x}<1$. Our analysis indicates that the model is
valid in a more restrictive range of $Q^{2}$. We also discuss the possibility
of incorporation of Froissart saturation condition in the model.
