Modal substructuring is an established subdomain of dynamic substructuring in which the handling of multi-point connections between subcomponents proves to be a problematic task. This is particularly the case with experimental models, where even small inconsistencies in the interface dynamics can greatly affect the accuracy of the substructuring process. An established solution to this problem is based on the projection of physical interface motion on the modal basis of one of the substructures. Although both the dimension and the origin of the projection basis prove to have a great impact on the accuracy of the substructuring prediction, the established procedures do not provide a general criterion for their appropriate selection. The aim of this paper is to propose an alternative weakening approach based on singular value decomposition (SVD) that enables the construction of a vector space and the establishment of a criterion for the selection of its dominant components. Considering two substructures involved in a certain step of a substructuring procedure, SVD is performed on the interface-related components of the substructures' concatenated modal bases. The dominant left singular vectors, therefore, embody the interface dynamics of both substructures and provide a consistent orthonormal basis for the constraint-weakening process. The proposed empiric criterion for estimating the required vector-space dimension is based on the magnitude of singular values. The efficiency of the proposed methodology is presented in comparison to the established modal-constraint approach with three numerical examples and an experimental-analytical transmission simulator coupling procedure. It is shown that the proposed singular vector constraint approach in conjunction with the criterion to estimate the weakening basis size, provides a consistent and reliable substructuring procedure.