  The decomposition of the nucleon spin into that of quarks and gluons is
related to twist-two GPDs according to Ji sum rule. Further decomposition into
the helicity and the orbital angular momentum inevitably requires twist-three
GPDs. In this paper we derive exact relations between twist-three GPDs and the
canonical orbital angular momentum density of quarks and gluons, and check
their consistency with the spin sum rule. Our work demonstrates that the
complete decomposition of the nucleon spin fits well with the framework of
perturbative QCD.
