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The discrete complex image method (DCIM) has been used extensively for the calculation of spatial-domain Green functions for one-layer or two-layer media. However, one difficulty in applying DCIM to general multilayered media is the lack of a reliable procedure for the extraction of surface wave components. In the paper, the spectral-domain potential Green functions for a general multilayered medium are reformulated so that their denominators are obtained in an iterative form. A two-stage root-searching procedure is proposed for seeking the roots of these denominators. The residuals associated with the surface wave poles are calculated through contour integration. Special methods for handling the branch cuts close to the surface wave poles are discussed. Numerical examples of different geometries are given to reveal the behaviour of the surface wave poles and verify the method.