A modified procedure is presented for assessing the seismic response of elastic non-proportionate multistory buildings. This procedure retains the simplicity of the methodology presented by the author in earlier papers, but it presents higher accuracy in buildings composed by very dissimilar types of bents. As a result, not only frequencies and peak values of base resultant forces are determined with higher accuracy, but also the location of the first mode center of rigidity (m1-CR). The closeness of m1-CR with the axis passing through the centers of floor masses (mass axis) implies a reduced rotational response and it is demonstrated that in elastic systemsa practically translational response is obtained when this point lies on the mass axis.Besides, when common types of buildings are detailed as planar structures under a code load, this response is maintained in the inelastic phase of their response as a result of the almost concurrent yielding of all the resisting bents. This property of m1-CR can be used by the practicing engineer as a guideline to form a structural configuration which will sustain minimum rotational response, simply by allocating the resisting elements in such a way that this point lies close to the mass axis. Inelastic multistory building structures, detailed as above, may be regarded as torsionally balanced multistory systems and this is demonstrated in eight story buildings, composed by dissimilar bents, under the ground motions of Kobe 1995 (component KJM000) and Friuli 1976 (component Tolmezzo E-W).