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In this paper, we present a technique for fingerprinting relational data by extending Agrawal et al.'s watermarking scheme. The primary new capability provided by our scheme is that, under reasonable assumptions, it can embed and detect arbitrary bit-string marks in relations. This capability, which is not provided by prior techniques, permits our scheme to be used as a fingerprinting scheme. We then present quantitative models of the robustness properties of our scheme. These models demonstrate that fingerprints embedded by our scheme are detectable and robust against a wide variety of attacks including collusion attacks.