In this paper, we propose a robust watermarking scheme called Double-Layer Spread-Transform Dither Modulation (DL-STDM) for watermarking motion data. We embed watermarks into the DCT domain of the quaternion logarithm image (QLI) representation of motion data. Experimental results demonstrate that our scheme is more robust than existing motion watermarking schemes against a wide variety of attacks, including noise addition, smoothing, cropping, attenuation, simplification, time warping, nonuniform scaling along amplitude axis and 2nd watermarking. Our scheme is useful for copyright protection and ownership identification of motion data.