  In this paper the theorems that determine composition laws for both cardinal
ordering permutations and their inverses are proven. So, the relative positions
of points in a hs-periodic orbit become completely known as well as in which
order those points are visited. No matter how a hs-periodic orbit emerges, be
it through a period doubling cascade (s=2^n) of the h-periodic orbit, or as a
primary window (like the saddle-node bifurcation cascade with h=2^n), or as a
secondary window (the birth of a $s-$periodic window inside the h-periodic
one). Certainly, period doubling cascade orbits are particular cases with h=2
and s=2^n. Both composition laws are also shown in algorithmic way for their
easy use.
