In the era of Big Data, relational data is at risk of piracy and misuse when distributed, shared and used. The use of digital watermarking technology is a reliable way to protect the copyright of relational data. In order to protect the copyright of relational data and recover the original data, many reversible watermarking schemes have been proposed in recent years, but most of them cannot extract the watermark information completely under severe attacks. To address this problem, a random-ized reversible watermarking scheme is proposed.Watermark embedding algorithm, watermark integrity checking algorithm, watermark detection algorithm and data recovery algorithm were designed. The watermark capacity is increased by embedding multiple watermarks in selected tuples, and the randomness of the watermark information distribution is increased by embedding unequal proportions of watermarks in different tuples. In extracting the watermark, the attacked bits are discarded to improve the accuracy of watermark detection. In addition, only a partition with complete watermark information is selected for watermark extraction. This not only improves the speed of watermark extraction, but also avoids the risk of key leakage from other partitions. The experimental results show that the complete watermark information can be extracted even when more than 90% of the tuples are under attack.