  In this paper decomposition of periodic orbits in bifurcation diagrams are
derived in unidimensional dynamics system $x_{n+1}=f(x_{n};r)$, being $f$ an
unimodal function. We proof a theorem which states the necessary and sufficient
conditions for the break-up of compound orbits in their simpler constituents. A
corollary to this theorem provides an algorithm for the computation of those
orbits. This process closes the theoretical framework initiated in (Physica D,
239:1135--1146, 2010).
