Recently watermarking algorithms of digital images based on singular value decomposition (SVD) have been proposed. Most SVD-based watermarking techniques use singular values as the embedding watermark information. These SVD-based techniques are advantageous for watermarking images since slight changes in the singular values do not significantly affect the image quality. However, it has been reported that these SVD-based watermarking algorithms, as implemented, suffer from a very high probability of false positive detections of watermarks. The false positive detection vulnerability of two recent SVD-based watermarking schemes is exposed. Two solutions are proposed to mitigate this vulnerability without changing the design principle of these watermarking algorithms.