We study the $p$-adic dynamical system generated by the (2-2) rational function $f(x)=\frac{ax^2}{1-x^2}$ with $a, x \in \mathbb{Q}_p$, which has three different fixed points. The behavior of these points depends on some conditions over $p$ and $|a|_p$, to be an attractor, indifferent or repellent point. We find these conditions, and also the basin of attraction and the Siegel disk, in each case.