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This paper proposes a boundary operation technique of two-dimensional (2D) non-separable oversampled lapped transforms (NSOLT). The proposed technique is based on a lattice structure consisting of the 2D separable block discrete cosine transform and non-separable redundant support-extension processes. The atoms are allowed to be anisotropic with the oversampled, symmetric, real-valued, compact-supported, and overlapped property. First, the blockwise implementation is developed so that the atoms can be locally controlled. The local control of atoms is shown to maintain perfect reconstruction. This property leads an atom termination (AT) technique as a boundary operation. The technique overcomes the drawback of NSOLT that the popular symmetric extension method is invalid. Through some experimental results with iterative hard thresholding, the significance of AT is verified.