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A higher-order Nyström scheme is developed for electromagnetic scattering by arbitrary conducting scatterers. In our implementation, we employ a superparametric geometry mapping for arbitrary curvilinear surfaces to minimize the geometry error. The local correction for singular integral kernels is manipulated efficiently with the Lagrange interpolation of the unknown functions followed by singularity extraction and Duffy's transformation. Since this local correction approach removes the local method of moments (MoM) procedure, the scheme is easier to implement and more efficient in controlling errors compared with other higher-order Nyström schemes. Two numerical examples for scattering by sharp-corner scatterers are conducted to demonstrate the robustness of this method.