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This paper presents an improvement to a decomposition scheme for the accurate classification of polarimetric synthetic aperture radar (POLSAR) images. Using a rotation of the coherency matrix to minimize the cross-polarized component, the four-component scattering power decomposition is applied to fully polarimetric SAR images. It is known that oriented urban area and vegetation signatures are decomposed into the same volume scattering mechanism in the previous decompositions and that it is difficult to distinguish vegetation from oblique urban areas with respect to the radar direction of illumination within the volume scattering mechanism. It is desirable to distinguish these two scattering mechanisms for accurate classification although they exhibit similar polarimetric responses. The new decomposition scheme by implementing a rotation of the coherency matrix first and, subsequently, the four-component decomposition yields considerably improved accurate results that oriented urban areas are recognized as double bounce objects from volume scattering.