Effective image retrieval by content requires that visual image properties are used instead of textual labels to properly index pictorial data. Shape is one of the primary low-level image features. Many shape representations had been proposed. The Zernike moment descriptor is the most suitable for shape similar-based retrieval in terms of computation complexity, compact representation, robustness, and retrieval performance. In this paper, we study the first 36 Zernike moments and find the dependence relations between them. A new compact representation is proposed to replace the old one. It is not only saving storage capacity but also reducing the execution time of index generation.