  In this paper we discuss the dynamical structure of the rational family
$(f_t)$ given by $$f_t(z)=tz^{m}\Big(\frac{1-z}{1+z}\Big)^{n}\quad(m\ge 2,~t\ne
0).$$ Each map $f_t$ has two super-attracting immediate basins and two free
critical points. We prove that for $0<|t|\le 1$ and $|t|\ge 1$, either of these
basins is completely invariant and at least one of the free critical points is
inactive. Based on this separation we draw a detailed picture the structure of
the dynamical and the parameter plane.
