The objective is a general damping correction procedure for determining the undamped modal parameters from damped system realization parameters. A discrete-time state-space realization of model test data is obtained using the eigensystem realization algorithm and polyreference, resulting in a set of difference equations. The realization is converted to continuous time, yielding a nominal first-order model. The common basis structural identification algorithm is used to obtain the normal mode frequences, mode shapes and damping ratios. In the case of nonproportional damping, a corrective transformation leads to correct structural normal modes and to nondiagonal modal damping matrix. Transformation introduced and constraints allow for a direct solution in the well-determined and overdetermined cases that requires only as many equations as the number of modes. The presented damping correction procedure is demonstrated through numerical examples. The advantages of developed method are as follows: 1) The displacement consistency criterion provides a constraint on the coupling transformation that helps to ensure the physical consistency of the transformation in the presence of experimental error. 2) In the case of overdetermined problem, the linearity of governing equations avoids the convergence problem for an iterative solution. 3) The application of the common base structural identification algorithm leads to an initial real-valued model that yields an estimate of desired normal models.