  We prove the integrability of the Yang-Baxter $\si$-model which is the
Poisson-Lie deformation of the principal chiral model. We find also an explicit
one-to-one map transforming every solution of the principal chiral model into a
solution of the deformed model. With the help of this map, the standard
procedure of the dressing of the principal chiral solutions can be directly
transferred into the deformed Yang-Baxter context.
