  We show that the third order approximation function $M_f$, proposed by S.
Amat, S. Busquier, S. Plaza, in \textit{J. Math. Anal. Appl.}, 366(2010),
24--32, for functions $f$ twice continuously differentiable and such that both
$f$ and its derivative do not have multiple roots, with at least four roots,
and infinite limits of opposite signs at $\pm\infty$, have periodic points of
any prime period and that the set of points $a$ at which the approximation
sequence $(M_f^n(a))_{n\in\mathbb{N}}$ does not converge is uncountable. In
addition, we observe that in their Scaling Theorem analyticity can be replaced
with differentiability.
