  We show that the Skyrme theory possesses a submodel with an infinite number
of local conserved currents. The constraints leading to the submodel explore a
decomposition of SU(2) with a complex field parametrizing the symmetric space
SU(2)/U(1) and a real field in the direction of U(1). We demonstrate that the
Skyrmions of topological charges $\pm 1$ belong to such integrable sector of
the theory. Our results open ways to the development of exact methods,
compensating for the non-existence of a BPS type sector in the Skyrme theory.
