The spreading out of internet these days has raised the worth of digital media all over the planet. Digital watermarking has been a boon to digital media world as it endows various benefits like authentication, copy control and rights management of digital media. Digital images a category under digital media can be watermarked either in time domain or in frequency domain. The goal is to produce an efficient, secure and invisible watermarked image using digital watermarking thereby improving the quality and increasing the robustness of watermarked image. Here, digital image is watermarked using wavelet transforms which is an efficient multi-resolution frequency domain techniques. The low frequencies of wavelet decomposition of the carrier image which is a color image is watermarked with a color logo shuffled using a chaotic map technique. Embedding process is highly secured as chaotic map technique shuffles the watermark in order to confuse any unauthorized person who tries to modify or remove the corresponding watermark. The Peak Signal to Noise Ratio (PSNR) of watermarked image has proved that the original image and the watermarked image are visually indistinguishable by human observers. Robustness is checked well by extracting the original watermark perfectly without any degradation in the original image.