Orthogonal moments have been extensively used as global feature-extraction descriptors in two-dimensional image reconstruction. However, a common problem for the existing image moments including orthogonal moments built in Cartesian coordinate system and radial orthogonal moments achieved at polar coordinate space is that Gibbs effect will occur, when image reconstruction is performed using features extracted from finite-order moments. It is well known that Gibbs noise can affect the capability of representation for image moments and the quality of reconstructed images. In this paper, we propose a set of novel orthogonal moments named as Walsh orthogonal moments (WOMs). The basis functions of Walsh orthogonal moments are Walsh functions, which composed of a class of complete orthogonal discontinuous binary function systems. Therefore, it provides possibility of avoiding calculating high order polynomials, and experimental results show Gibbs noise can be efficiently avoided by using discontinuous functions as the basis functions of Walsh orthogonal moments.