Interaction energy between two localized moments is calculated on the tight-binding or Wolff-Clogston model by using the Hartree-Fock approximation. A simple general expression is obtained for the effective exchange energy between a distant pair of moments which generally decays as R-3 with the oscillations given by the stationary radii of the Fermi surface. Interaction between an adjacent pair of moments is shown to be of local character and its sign is primarily governed by the electronic occupation in the impurity states. A general rule for the sign of the coupling between two moments proposed earlier on the basis of the Anderson model is strongly supported. Possible discontinuous occurrence of localized moments in some alloys is also discussed on the same model.