Digital watermark has been proposed as the means for copyright protection of multimedia data in network-based distribution framework. However, existing digital watermarking mechanisms have some problems that they cannot resolve the rightful ownership alone. Specially, someone can provide counterfeited watermark which can be performed on a watermarked image to allow multiple claims of rightful ownership. In this paper, we use designated verification method for undeniable signatures in the watermarking process. The confirmer of watermark can sure that only the intended verifier(s) can be convinced about the validity or invalidity of the signature. We then propose more secure watermarking method while keeping efficiency of well-known class of watermarking schemes. This first protects the re-watermarking attack. Using this scheme, the security of many watermark-based applications can be significantly improved.