In the present paper a new displacement method, defined as external variables one, is proposed inside the multidomain symmetric Boundary Element formulation. This method is a natural evolution of the displacement approach with interface variables in the multidomain symmetric BEM analysis. Indeed, the strategy employed has the advantage of considering only the kinematical quantities of the free boundary nodes and the algebraic operators involved show symmetry and very small dimensions. The proposed approach is characterized by strong condensation of the mechanical and kinematical boundary nodes variables of the macro-elements. All the domain quantities, such as tractions and stresses, displacements and strains, are computed through the Somigliana Identities in a subsequent phase. Some examples are shown using the calculus code Karnak.sGbem, by which it was possible to make some comparisons with analytical solutions andothe rapproaches to show the effectiveness of the method proposed