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A new class of analytical absorbing boundary conditions (ABCs) for the truncation of the finite-difference time-domain (FDTD) lattice is introduced. These ABC originate from the exact impedance boundary operator and contain both electric and magnetic fields. The performance of the proposed second-order ABCs is studied with a two-dimensional FDTD program. The results indicate that the proposed ABCs work approximately as well as the third-order analytical ABCs, even if they are essentially as easy to implement as the second-order Mur ABC. Also, in this paper, the relation between the so-called Engquist-Majda operator for the absorption of plane waves and the exact surface impedance boundary condition is discussed.