The False Positive Problem (FPP) is one of the main concerns in Singular Value Decomposition (SVD) based image watermarking schemes. In the SVD transform, an image is decomposed into three matrices: \(\textsf{U}\) and \(\textsf{V}\) (singular vectors) and \(\textsf{S}\) (singular values). The coefficients within \(\textsf{S}\) are excellent candidates for watermark insertion due to their stability against signal processing and geometric attacks. However, this embedding is not applicable for copyright protection since attackers can misuse of FPP. In this paper, we designed and implemented an independent full package as an authentication system to investigate the authenticity of watermark extractors and ensure FPP elimination. This authentication system can be added to all SVD based image watermarking schemes suffering from FPP to eliminate it and to ensure security with minimum degradation in imperceptibility and robustness. The distinction of the proposed system is that it can be offered as a separate and independent package for authentication without tangible consequence on quality of the watermarked images which is especially useful for all watermarking schemes susceptible to FPP to correct false positive and avoid false negative problems.