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A new (under practical circumstances ideal) absorbing boundary condition (ABC) to terminate homogenous waveguides for use with the FDTD method is presented. The ABC uses a numerical Green's function to achieve a reflection error of the same order of magnitude as the precision of the used floating point type. The use and implementation of this waveguide termination is straight forward and the storage and runtime requirements are small compared to the overall requirements for FDTD simulations. The FDTD method incorporating the new ABC was applied to true three dimensional waveguide junctions. The obtained results show good agreement with previously published results.