  J.Ritt has investigated the structure of complex polynomials with respect to
superposition. In particular, he listed all the polynomials admitting different
double decompositions into indecomposable polynomials. The analogues of Ritt
theory for rational functions were constructed just for several particular
classes of the said functions, say for Laurent polynomials (F.Pakovich). In
this note we describe a certain class of double decompositions for rational
functions. Essentially, described below rational functions were discovered by
E.I.Zolotarev in 1877 as a solution of certain optimization problem. However,
the double decomposition property for them was hidden until recently because of
somewhat awkward representation. We give a (possibly new) symmetric
representation of Zolotarev fractions resembling the parametric representation
for Chebyshev polynomials, which are a special limit case of Zolotarev
fraction.
