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In this paper, an extension of CPT scheme (CPTE for short) is introduced. In watermarking area, this is a block-based approach. Given a binary image B, in each block F of a size mÃn of B, by CPT scheme, ones can embed r = Round(log2(m.n+1)) bits by changing at most two entries of F. In our CPTE scheme, r = Round(log2(m.n)) + 1 bits can be embedded by changing at most two entries of F, too. That means, in most cases, the number of embedded bits given by our CPTE scheme is larger than that by CPT scheme one bit. As a consequence, we establish a new modified scheme-MCPTE based on CPTE scheme to control the quality for security of the embedded blocks, in the same way due to [Tseng-Pan, 2001]. Experimental results show that in general, MCPTE scheme gives more embedded bits than those by Tseng-Pan' scheme, while the quality is the same.