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 (SOE) requires that the spin current, charge current and spin orientation are all orthogonal to each other. Here we show the observation of a SOE near the NM/FM interface that exhibits a very different symmetry from the conventional spin Hall effect, insofar as the spin polarization is further rotated 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 greatly benefit the development of magnetic memories.