  In this paper we give a combinatory proof of the Lie bialgebra structure
presented in the vector space of reduced cyclic words. This structure was
introduce by M. Chas in Combinatorial lie bialgebras of curves on surfaces,
where the proof of the existence of this Lie bialgebra structure is based on
the existence of an isomorphism between the space of reduced cyclic word and
the space of curves on a surface.
