ABSTRACT: The relative motion of an arbitrary asymmetrical rigid body in this article is studied. Three new additional kinematic characteristics are defined, namely, vectors-real absolute, transmissive, and relative generalized velocity. A new theorem for summation of the rigid body’s real generalized velocities, with these new additional kinematic characteristics, is formulated. Using the final differential equations of absolute rigid body motion, which have been obtained in previous author articles, the differential equations describing the rigid body relative motion in a matrix form are obtained. These equations are suitable for a numerical solution using specialized mathematical programs.