An improved technique for synthesizing the modes obtained with fixed interface coordinates is proposed. The reduction in the size of a substructure model is achieved through a higher order mode superposition approach. For the first time, an analytical rationale for the popular Craig-Bampton-Hurty method is presented. It is shown that the Craig- Bampton-Hurty method is a special case of the proposed method. The proposed approach can be used to improve the accuracy of the calculated eigenproperties by utilizing the higher order component modes but without calculating additional normal modes of the substructures.