Robust as well as secure image watermarking is capable of providing a promising solution in many copyright protection applications. In this paper, an improved image watermarking scheme based on DFT with a decomposition algorithm is proposed. First, two dimensional (2D) Fast Fourier Transform (FFT) is applied to the host image, and then its singular value decomposition (SVD) is performed. Second, the watermark image is encrypted with a chaotic map for ensuring security against unauthorized detection, and then its 2D FFT and SVD are also performed. Third, the singular values of the watermark image are embedded into the singular values of the host image. The hybridization of DFT with SVD ensures the increasing performance of the watermarking system from the perspectives of visual distortion and robustness. Experimental results show that our proposed method is highly robust and also imperceptible with a large watermark size and increased security than the classical DFT-based methods.