We introduce a previously unknown spin-related transport phenomenon, consisting of a transformation (swapping) of spin currents, in which the spin direction and the direction of flow are interchanged. Swapping is due to the spin-orbit interaction in scattering. It originates from the correlation between the spin rotation and the scattering angle. This effect is more robust than the skew scattering, since it exists already in the first Born approximation. Swapping may lead to the spin accumulation with spin polarization perpendicular to the surface, unlike what happens in the spin Hall effect.