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The time-domain discrete Green's function of the external region beyond a given boundary has been recently introduced as a discretized version of the impedance condition. It is incorporated within the framework of the finite-difference time-domain (FDTD) as a quasi-local, single-layer boundary condition, termed the Green's function method (GFM). The stability characteristics of this method are provided. The analysis is based on the general representation of the method in matrix form, whose eigenvalues are investigated. This formulation helps detect and remove possible instabilities of the algorithm. A demonstration of the ability of the GFM absorbing boundary condition (ABC) to deal with re-entrant corner problems is given.