The spin–orbit interaction enables interconversion between a charge current and a spin current. It is usually believed that in a nonmagnetic metal (NM) or at a NM/ferromagnetic metal (FM) bilayer interface, the symmetry of spin–orbit effects requires that the spin current, charge current, and spin orientation are all orthogonal to each other. Here we demonstrate the presence of spin–orbit effects near the NM/FM interface that exhibit a very different symmetry, hereafter referred to as spin-rotation symmetry, from the conventional spin Hall effect while the spin polarization is rotating about the magnetization. These results imply that a perpendicularly polarized spin current can be generated with an in-plane charge current simply by use of a FM/NM bilayer with magnetization collinear to the charge current. The ability to generate a spin current with arbitrary polarization using typical magnetic materials will benefit the development of magnetic memories.