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Using an alternative source decomposition, we propose new exact boundary conditions on numerical boundary of a square lattice for out-of-plane motion over the whole space. A set of recurrence relations are found for the resulting kernel functions, hence allow their efficient and accurate evaluation with a system of ordinary differential equations. Stability of the boundary conditions is proved rigorously. Numerical results illustrate effective suppression for spurious wave reflection, and elimination of corner effects. This approach may be extended to other lattice structures and in higher dimensions. [ABSTRACT FROM AUTHOR]