An outer race for a rocker bearing includes an internal sliding layer and an external support layer, wherein the sliding layer and the bearing layer are formed from a wound composite fiber material. The outer race is identified by exactly one parting line. A rocker bearing with such an outer race and a method for its production is also provided, in which a sliding layer and a support layer of synthetic resin impregnated fibers are wound in succession onto a winding mandrel, and outer races are formed after setting on the winding body thus produced. The sliding layer and the support layer are wound onto a cylindrical winding mandrel, and the outer race is provided with exactly one parting line opening it, and sliding layer material on its inside is removed to such an extent that a partially spherical contour is obtained for receiving a complementary inner race.