  A new recursive function on discrete interval exchange transformation
associated to a composition of length $r$, and the permutation $\sigma(i) = r
-i +1$ is defined. Acting on composition $c$, this recursive function counts
the number of orbits of the discrete interval exchange transformation
associated to the composition $c$. Moreover, minimal discrete interval
exchanges transformation i.e. the ones having only one orbit, are reduced to
the composition which label the root of the Raney tree. Therefore, we describe
a generalization of the Raney tree using our recursive function.
