On The Dynamics Of The Rational Family ${\mathbf{f}}_{\mathbf{t}}(\mathbf{z})=-\frac{\mathbf{t}}{\mathbf{4}}\frac{({\mathbf{z}}^{\mathbf{2}}-\mathbf{2}{)}^{\mathbf{2}}}{{\mathbf{z}}^{\mathbf{2}}-\mathbf{1}}$

In this paper we discuss the dynamics as well as the structure of the parameter space of the one-parameter family of rational maps $\ds f_t(z)=-\frac{t}{4}\frac{(z^{2}-2)^{2}}{z^{2}-1}$withfreecriticalorbit$\pm\sqrt{2}\xrightarrow{(2)}0\xrightarrow{(4)}t\xrightarrow{(1)}…$. In particular it is shown that for any escape parameter $t$ the boundary of the basin at infinity ${\text{A}}_t$ is either a Cantor set, a curve with infinitely many complementary components, or else a Jordan curve. In the latter case the Julia set is a Sierpi'nski curve.