This paper presents a novel approach to normalize binary shapes which is based on the Radon transform. The key idea of the paper is an original adaptation of the Radon transform. The binary shape is projected in Radon space for different levels of the (3-4) distance transform. This decomposition gives rise to a representation which has a nice behavior with respect to common geometrical transformations. The accuracy and the efficiency of the proposed algorithm in the presence of a variety of transformations is demonstrated within a shape recognition process.