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We modify the 2D explicit isotropic-dispersion finite-difference time-domain (ID-FDTD) scheme originally proposed for lossless media , which can drastically improve the accuracy of the 2-D ID-FDTD scheme for lossy media. The proposed scheme adopts new scaling factors for material properties such as the permittivity, permeability and conductivity. The new scaling factors can generate nearly the exact phase velocity and attenuation factor of a lossy medium for a single frequency. For the validation of the proposed scheme, two scattering problems are considered.