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Numerical instability occurs in analyses of an electromagnetic and structural coupled problem or a magnetic damping problem when the matrix equations of structure and eddy current are solved alternately. In this paper, an augmented staggered method is proposed for the coupled analysis. The stability of this method is demonstrated for the magnetically damped vibration by finite element analyses. According to the characteristic equation obtained from the recurrence relation of this time integration scheme, it is confirmed that this method is unconditionally stable for the intensity of magnetic field and the size of time increment.