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Discrete orthogonal moments have several computational advantages over continuous moments. However, when the moment order becomes large, discrete orthogonal moments (such as the Tchebichef moments) tend to exhibit numerical instabilities. This paper introduces the orthonormal version of Tchebichef moments, and analyzes some of their computational aspects. The recursive procedure used for polynomial evaluation can be suitably modified to reduce the accumulation of numerical errors. The proposed set of moments can be used for representing image shape features and for reconstructing an image from its moments with a high degree of accuracy.