We find the angular momentum L of a point particle with electric charge e held at a fixed position in the presence of a black hole with magnetic charge g. (For a point charge in the presence of an ordinary magnetic monopole, it is known that L = eg.) The angular momentum does depend on the separation distance between the particle and the black hole; however, L --> eg for a large separation. Implications for the cosmic censorship hypothesis, the quantum hairs and other physical situations are discussed.