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This paper investigates the problem of data hiding for binary images authentication in morphological binary wavelet transform domain. Directly using the detail coefficients as a location map to determine the data hiding locations is difficult to achieve blind watermark extraction. Hence, we view flipping an edge pixel as shifting the edge location one pixel horizontally and vertically. Based on this observation, we propose an interlaced transform to track the shifted edges. Different from existing block-based approach, in which the block size is constrained by not less than 3 x 3, we process the image in 2 x 2 blocks. The two processing cases that the flippantly condition of one is not affected by flipping the candidates of another are combined such that an extremely large capacity can be achieved, which slightly sacrifices the visual quality.