  The orbital energy and momentum of the compact binary systems will loss due
to gravitational radiation. Based on the mass and mass-current multipole
moments of the binary system with the spin vector defined by Boh\'{e} et al.
[Class. Quantum Grav. 30, 075017 (2013)], we calculate the loss rates of
energy, angular and linear momentum induced by the next-to-leading spin-orbit
effects. For the case of circular orbit, the formulations for these losses are
given in terms of the orbital frequency.
