Super-attracting periodic orbits for a classical third order method

We use a classical third order root-finding iterative method for approximating roots of nonlinear equations. We present a procedure for constructing polynomials so that super-attracting periodic orbits of any prescribed period occur when this method is applied. This note can be considered as the second part of our previous study [S. Amat, S. Busquier, S. Plaza, A construction of attracting periodic orbits for some classical third order iterative methods, J. Comput. Appl. Math. 189(1–2) (2006) 22–33].