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This letter presents a novel steganography scheme capable of concealing a piece of critical information in a host message which is a binary image (e.g., a facsimile). A binary matrix and a weight matrix are used as secret keys to protect the hidden information. Given a host image of size m×n, the proposed scheme can conceal as many as └log2 (mn+1)┘ bits of data in the image by changing, at most, two bits in the host image. This scheme can provide a higher security, embed more information, and maintain a higher quality of the host image than available schemes.