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Being extremely precise and at a low loss of perceptual quality, the attacks of value modification and optimized noise reduction still threaten the watermarking based on quantization index modulation (QIM). To resist them, the paper constructs a non-uniform discrete cosine transform (NDCT), and brings out an NDCT-QIM watermarking scheme, which embeds a watermark in a private NDCT domain with the parameters of NDCT as a secret key. The technique blinds the value modification by dispersing the attacking signal and changing its energy in the embedded domain. Because of the variable power spectrum of a watermark, the noise reduction becomes non-optimal. Some other advantages, including the ease of embedding, computational simplicity, etc., can also be acquired or maintained by the use of NDCT.