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The discrete two‐dimensional (2D) S‐transform (ST‐2D) is a space‐frequency representation that provides the local spectrum at each pixel in an image. The inherent localisation properties of the ST‐2D make it a preferred candidate for space‐frequency analysis. However, the ST‐2D is sensitive to the image rotation. This limits its use in many image processing applications such as texture analysis. This study describes the rotational sensitivity of the ST‐2D, and explains how this limits its application. To overcome these problems, a novel rotationally invariant S‐transform (RIST) is formulated, and its rotational invariance is investigated. The RIST can provide approximate rotational invariance for magnitudes and complex values over a wide range of rotation angles, but with a trade‐off of higher computation time. The RIST may be useful for many medical, scientific and industrial applications. [ABSTRACT FROM AUTHOR]