Standard approaches to domain decomposition methods (DDM) are uncapable of producing block-diagonal system matrices. The derived-vector-space (DVS), approach to DDM, introduced in 2013, overcomes this limitation. However, the DVS approach in its original form was applicable to a relatively narrow class of problems because it required building a special matrix, whose construction is frequently impossible. In this paper, an enhanced formulation of DVS is presented, which does not require the construction of a special matrix and is applicable to any linear problem. Keywords: domain decomposition, parallel processing, DVS, FETI, BDDC