The many-body symmetry-adapted perturbation theory (SAPT) of intermolecular interactions has been applied to the nonadditivity of the trimer first-order exchange energy. The orbital expressions including intramonomer correlation effects up to the second order have been derived. These expressions, together with other many-body SAPT terms developed earlier, have been used to compute the nonadditivity of the helium trimer. The computed points have been fitted by a global potential function.