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A new hybrid numerical method is described for scattering from an electrically large perfectly-conducting object with dihedral effects above a very long one-dimensional rough surface (two-dimensional problem). Such a problem involves a large number of unknowns and cannot be solved easily with a conventional method of moments by using a direct LU inversion. Thus, to solve this issue, the Extended-PILE method is combined with the forward-backward spectral acceleration (FBSA) for the local interactions on the rough surface and with the second-order physical optics (PO2) approximation for the local interactions on the object. Classically objects under test do not present dihedral effects and in the high frequency domain the first-order PO (PO1) provides the main contribution. In opposite, in this paper since a cross is considered, the second-order inner reflections contribute significantly and the PO2 must be included. By assuming a Gaussian process with a Gaussian height spectrum, this new hybrid method, E-PILE+FBSA+PO2, is tested against the rigorous E-PILE+ FBSA method (direct LU inversion on the object) as functions of the object inclination, the polarization and the incidence angle.