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This paper present an efficient technique for the analysis of electromagnetic scattering by a conducting sphere coated with uniaxial anisotropic media. The technique is based on the method of higher order MoM of the surface integral equations. This higher order MoM solution uses the higher order hierarchical basis functions which are based on the modified Legendre polynomials. Numerical examples results are given to demonstrate that the higher order hierarchical basis functions are accurate and efficient in the calculations of anisotropic uniaxial-coated conducting objects. The number of unknowns decreases dramatically.