Digital Watermarking is used for copyright protection and authentication of digital media-image/audio/video data. In this paper, a novel dual watermarking scheme is described based on Discrete Wavelet Transforms (DWT) and Singular Value Decompositions (SVD). Unlike the existing dual watermarking schemes, both the watermark embedded using DWT and SVD are invisible in the proposed scheme. For embedding, both the images are transformed into Wavelet domain and SVD is performed further on both the images. Subsequently the singular values are summed up to find the new set of singular values. Both the watermarks get embedded in the same manner. A reliable watermark extraction scheme has been developed for the extraction of the watermarks from the distorted image. Experimental evaluation demonstrates that the proposed scheme is capable of withstanding variety of attacks.