Displacements of the energy centroids of the distinct isospin fragments of the isovector giant resonances of nuclear multipole excitations are obtained within the framework of an isoinvariant RPA. The isovector contribution of the displacements is shown to be independent of the ground-state correlations (GSC) as well as of the multipolarity, whereas the isotensor contribution is found to have a simple dependence on multipolarity and a very vital dependence on the GSC. The latter comes out to be in quantitative agreement with an independent estimate by Lane and Mekjian (1981). It is also shown that, for the spurious (isoscalar dipole) excitation, the well known vanishing excitation energy would lead to vanishing strength as well. The two parameters measuring the above contributions have been estimated numerically, using a few well established model and empirical parameters, and the results agree quite well with the existing experimental findings. These also include confirmation of multipolarity independence of the isovector contribution and the essentially renormalising effect of the isotensor contribution.