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FDTD solutions have their own properties distinct from the discrete samples of corresponding continuous wave solutions. Thus, the discrete equivalent to the Green's function is needed for applications like the one using a hybrid absorbing boundary condition which couples the FDTD algorithm with integral operators for nonconvex scatterers. In this paper we propose a new closed-form expression for the 3-D dyadic FDTD-compatible Green's function in infinite free space via a novel approach with the ordinary z-transform along with the spatial partial difference operators. The final expression involves a summation of standing wave modes with time-varying coefficients. The propagation of waves in the Yee's grid can be interpreted by the selective property of the time-varying coefficients, which is very different from the conventional concept of a traveling wave. The traditional dispersion analysis using plane waves for the FDTD algorithm in a source-free region may not be applicable to explain the wave propagation phenomenon through our analytic expression, because the corresponding z-transform diverges for z on the unit circle.