A new tensor expansion of the orbit–orbit interaction is derived straightforwardly in a form which is compact and completely symmetric in the coordinates of interacting particles. The m-scheme matrix element of the orbit–orbit interaction is then obtained as a concise sum of radial integrals. The graphical form of the m-scheme matrix element is also presented, which enables one to obtain graphically many-particle matrix elements from easily constructed diagrams. Graphical analysis of different contributions to the orbit–orbit interaction in a many-particle system is demonstrated by several examples.