The authors consider a discrete dynamical system defined in the following way: Starting with a base triangle \(\Delta_0=ABC\), erect externally on all sides of \(\Delta_0\) similar isosceles triangles with apex angle \(\pi-2\theta_0\). The apices opposite to \(A\), \(B\) and \(C\), say, \(A_1,B_1,C_1\) determine the \textit{Kiepert triangle} \(\Delta_1\). Then iterate the process with \(\Delta_1\) and apex angle \(\pi-\theta_1\) and so on\dots In the paper under review, it is shortly proved that the above construction has an equilateral limit when the apex angles are all equal and nonstraight (this was known). The convergence of the construction is also studied under other choices for the sequence \(\theta_0,\theta_1,\dots\).