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A four-component model-based decomposition for polarimetric synthetic aperture radar (SAR) images is proposed to deal with the ground objects with orientation angles around 45°. In the previous decompositions, these special targets are mixed with the vegetated areas. With the deficiency of the previous decompositions analyzed, the ambiguity between two scattering mechanisms is clarified. A rotated Fresnel dihedral reflection model is introduced in the proposed algorithm, to model the scattering characteristics of these special targets. The nonnegative eigenvalue decomposition is applied to the remainder coherency matrix to prevent negative powers of the decomposed scattering mechanisms. Another advantage of the proposed decomposition is that it makes use of all the information provided by the coherency matrix, which remains unachieved in the previous model-based decompositions. Experimental Synthetic Aperture Radar (E-SAR) L-band polarimetric SAR data acquired over Oberpfaffenhofen, Germany, are analyzed in this letter. Experimental results indicate that the special ground objects have acquired correct scattering mechanisms, which verifies the effectiveness of the proposed method.