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In this paper we present a new technique for reducing the discretization error in the transmission line matrix (TLM) method at arbitrarily shaped interfaces between two contrasting media. TLM employs cuboid mesh elements which are not conformal with curved or slanted interfaces, resulting in stair-casing and a potentially large modeling error. This error can be reduced by an order of magnitude through modification of the constitutive parameters of cells that straddle an interface between two media. Novel expressions for this modification procedure are derived and validated in this paper.