  We present the theorem which determines, by a permutation, the cardinal
ordering of fixed points for any orbit of a period doubling cascade. The
inverse permutation generates the orbit and the symbolic sequence of the orbit
is obtained as a corollary. The problem present in the symbolic sequences is
solved. There, repeated symbols appear, for example, the R (right), which
cannot be distinguished among them as it is not known which R is the rightmost
of them all. Therefore, there is a lack of information about the dynamical
system. Interestingly enough, it is important to point that this theorem needs
no previous information about any other orbit.
