Research efforts in the field of digital watermarking are increasing fast all over the world. As a result, a lot of new watermarking technologies are being developed. On the other hand, some researchers are also investigating different ways of attacking digital watermarks. In this paper we propose a new attack for public watermark schemes with the second watermark. The proposed attack requires neither algorithmic knowledge of the watermarking technology nor the watermarking key. To illustrate the performance of the proposed attack we applied it to two commercial watermarking scheme, Picturmarc and Suresign. The experiments showed that the attack is very effective in impairing the detection of embedded watermark. In addition, we have a closer look at application dependent implications of this new attack