Let \(f(z)\), \(g(z)\) be power series \(f(z)=\sum_{n\geq 0}f_ nz^ n\), \(g(z)=\sum_{n\geq 0}g_ nz^ n\), let \(r_ f\), \(r_ g\) be their radii of convergence, and let \[ h(z)=\sum_{n\geq 0}h_ nz^ n \] be their Hadamard composition. Then \(r_ h\geq r_ fr_ g\). The authors prove the following. Theorem. Let \(r_ h=r_ f=r_ g=1\). If (a) the function \(f(z)\) has the unique singularity \(z=1\) on the unit circle, (b) \(\text{Re}\,g_ n\geq 0\), \(n=0,1,2,\ldots\), (c) \(\lim_{n\to \infty}[\frac{\text{Re}\,g_ n}{| g_ n|}]^{1/n}=1\), then \(z=1\) is a singular point of \(h(z)\). The analogous theorem was formulated in the well-known book of \textit{L. Bieberbach} [Analytische Fortsetzung. Russ. transl. (1955; Zbl 0174.36801)] without the condition (c). The authors construct a counterexample of such a statement. The authors also prove that the condition (c) in the assumptions of the theorem may be replaced by one of the two weaker conditions: \[ (c')\quad\text{Im}\, g_ n=O(\text{Re}\, g_ n),\quad n\to \infty,\quad (c'')\quad \lim_{n\to \infty}[\text{Re}\,g_ n]^{1/n}=1. \]