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The performance of an automatic hand geometry authentication system relies heavily on the quality of the captured hand images. Factors related to the acquisition device (e.g. dirty scanner surface) or the user-sensor interaction process (e.g. hand positioning) can degrade the quality of the acquired sample. Therefore, upon capture of a hand sample it is important to assess its validity. In this paper, an invalid sample detection module based on geometric constraints is presented. The experimental setup consists of a hand geometry verification system tested in two different acquisition scenarios: BiosecurID (400 users, scanner) and Biosecure (210 users, camera). Results confirm a noticeable improvement in the system performance as the fraction of invalid samples rejected increases. In particular, discarding about 5 percent of the images in BiosecurID produces an improvement from 2.8 % EER to 0.1% EER.