This study reviews the superiority and limitations of the Singular Value Decomposition (SVD)-based video watermarking scheme. First applies key frame selection to the video sequence to obtain an appropriate video frame for the purpose of watermark embedding in this paper. The Fibonacci-Lucas image transformation scrambles the grayscale watermark image before the embedding process. The former scheme satisfies the imperceptibility and robustness aspects. However, it can suffer from the False-Positive-Problem (FPP) in which a counterfeit watermark image can be easily reconstructed by a malicious attacker. This study presents a new technique for overcoming the FPP of the aforementioned scheme. The proposed method embeds the principal components of the watermark image rather than the Singular Value Matrix (SVM) into the host video. As results, the proposed methods yield promising results in terms of imperceptibility as well as robustness. At the same time, it solves the FPP. A theoretical analysis of embedded watermark information is also provided in this work. The theoretical analysis meets the experimental-based results in the SVD-based video watermarking scheme. INDEX TERMS False-positive-problem, watermarking, principal components, Fibonacci-Lucas transform, vulnerability attack.