An identification procedure to improve the mass-weighted orthogonality of measured mode shapes is introduced. The procedure takes into account the degree of mode isolation present during measurement. This is accomplished by establishing a set of new mode shapes, from the measured vectors, that satisfy cross-orthogonality constraints and are a minimum deviation from the measured data. A significant feature is that each measured mode, from which improved modes are identified, can be established using different excitation locations and force levels. This allows the procedure to improve the isolation of modes measured with multishaker sine-dwell testing techniques. Nomenclature [A]j = defined in Eq. (19) [B]j = defined in Eq. (19) [C]j = defined in Eq. (19) [C}j = defined in Eq. (15) [F] = excitation force levels Fje =j! element of [F] [G]j = defined in Eq. (19) [G]j =yth column of [G] [H]j = defined in Eq. (19) [7\j = defined by Eq. (12) L = Lagrange function [M] =mass matrix [ w\ = weighting matrix oijj = defined by Eq. (4) [0] = eigenvalues of [0] T[M] [0] f = critical damping ratio [0] = eigenvectors of [0] T[M] [0] [X] = matrix of Lagrange multipliers X^ = element of & of [X], Lagrange multiplier [\}j =yth row of [X] [$] = all the normal modes of a structure [0] = identified mode shapes [0] = analytically orthogonalized mode shapes [0m] = measured modes [0]y =yth column of [0] 0/A: =jk element of [0] 0$ =jk element of [0 m] M = defined by Eq. (17) [fi] = admittance matrix, imaginary components Q// = U element of [ft] [Q\l = defined in Eq. (9) coy = frequency of excitation, rad/s