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Digital video is one of the popular multimedia data exchanged in the internet. Due to their perfectly replicable nature many illegal copies of the original video can be made. Methods are needed to protect copyrights of the owner and prevent illegal copying. A video can also undergo several intentional attacks like frame dropping, averaging, cropping and median filtering and unintentional attacks like addition of noise and compression which can compromise the owner information thereby denying authentication. In this paper, a robust Discrete Wavelet Transform (DWT)-based blind digital video watermarking scheme with scrambled watermarks based on scene changes has been proposed for authentication of digital video, which embeds different parts of a single watermark into different scenes of a video. The video watermarking algorithm is robust against the attacks of frame dropping, averaging and compression, which are considered as some of the common types of attacks applied particularly on the video and due to the use of DWT it can also withstand geometrical attacks making the watermark perceptually invisible. Furthermore, it allows blind retrieval of embedded watermark which does not need the original video. The proposed algorithm has been compared with an existing DWT based watermarking scheme and is found to exhibit better robustness.