This paper presents a method for treating complex structures as assemblies of distinct substructures, using basic mass and stiffness matrices for each substructure. The method employs two forms of generalized coordinates: boundary generalized coordinates for displacements and rotations along substructure boundaries, and substructure normal-mode generalized coordinates for free vibration modes relative to completely restrained boundaries. The boundary generalized coordinates are related to the "constraint modes" of the substructures, which are generated through matrix operations from substructure input data. The substructure normal-mode generalized coordinates are related to the normal modes of the substructures. The definition of substructure modes and the requirement of compatibility along substructure boundaries lead to coordinate transformation matrices that are used to obtain the system mass and stiffness matrices from the substructure matrices. A Rayleigh-Ritz procedure is used to reduce the total number of degrees of freedom while retaining accurate dynamic behavior. The method allows for substructure boundaries with any degree of redundancy and is demonstrated through a free vibration analysis of a structure with a highly indeterminate substructure boundary. The paper also discusses the advantages of the method, including easier formulation, more compact presentation, simplified computer programming, and potentially shorter computer times.This paper presents a method for treating complex structures as assemblies of distinct substructures, using basic mass and stiffness matrices for each substructure. The method employs two forms of generalized coordinates: boundary generalized coordinates for displacements and rotations along substructure boundaries, and substructure normal-mode generalized coordinates for free vibration modes relative to completely restrained boundaries. The boundary generalized coordinates are related to the "constraint modes" of the substructures, which are generated through matrix operations from substructure input data. The substructure normal-mode generalized coordinates are related to the normal modes of the substructures. The definition of substructure modes and the requirement of compatibility along substructure boundaries lead to coordinate transformation matrices that are used to obtain the system mass and stiffness matrices from the substructure matrices. A Rayleigh-Ritz procedure is used to reduce the total number of degrees of freedom while retaining accurate dynamic behavior. The method allows for substructure boundaries with any degree of redundancy and is demonstrated through a free vibration analysis of a structure with a highly indeterminate substructure boundary. The paper also discusses the advantages of the method, including easier formulation, more compact presentation, simplified computer programming, and potentially shorter computer times.