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In this study, the concept of fractional wavelet packet transform is explored with its application in digital watermarking. The core idea of the proposed watermarking scheme is to decompose an image via fractional wavelet packet transform and then a reference image is created by changing the positions of all frequency sub-bands at each level with respect to some rule which is secret and only known to the owner/creator. For embedding, the reference image is segmented into non-overlapping blocks and modify its singular values with the watermark singular values. Finally, a reliable watermark extraction algorithm is developed for the extraction of watermark from the distorted image. The feasibility of this method and its robustness against different kind of attacks are verified by computer simulations.