Many Japanese animation products benefit from the techniques of computer graphics. In the animation process, three-dimensional (3D) characters are often rendered so that the characters move according to a Japanese traditional animation style called limited animation or anime. The hair of the characters is modeled as a set of bunches and the motion of each bunch should also be defined in the manner of limited animation, which is different from its physically correct motion. We present a method to produce a hair motion for 3D characters that is appropriate for limited animation under the assumptions that the hair motion is periodic and other objects, including the camera, remain stationary. We present a mathematical formulation of this hair motion based on a typical technique used in traditional hand-drawn anime and apply the motion to each bunch of hair of an example 3D character.