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Watermarking, in particular, is identified as a major technology to achieve copyright protection and multimedia security. In this study, combination of Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) via Lower-and-Upper (LU) Decomposition is proposed as a new watermarking algorithm with a chaotic map approach called Arnold's Cat Map (ACM). Similarity Ratio (SR) and Peak Signal-to-Noise Ratio (PSNR) values in this algorithm, as quality metrics, are greater than that of in the algorithms without chaotic mapping. Apart from robustness, imperceptibility, reliability, and security; the other novel side of this study is to expand the application areas of watermarking with a new algorithm consisting DWT, SVD, and LU with ACM together.