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Summary form only given. This paper aims to improve the accuracy of watermark detection in correlation-based watermarking methods for images. In the correlation-based watermarking method, watermark detection is carried out by computing the correlation between a watermarked image and a pseudorandom code to be checked for its presence. Hence its accuracy depends on the characteristics of host images. In this paper, we first show an experimental result that a certain image may cause watermark detection errors. Then we develop an improved version of the watermark embedding process to be effective in such a situation. The improvement is accomplished by designing a whitening filter using a nonlinear programming algorithm. Numerical experiments show good performance as expected by us.