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The normalization of a binary shape is a necessary step in many image processing tasks based on image domain operations. When one must deal with deformable shapes (due to the projection of non-rigid objects onto the image plane or small changes in the position of the view point), the traditional approaches doesn't perform well. This paper presents a new method for shape normalization based on robust statistics techniques, which allows to keep the location and orientation of shapes constant independent of the possible deformations they can suffer. A numerical comparison of the sensitivity of both methods is used as a measure to validate the proposed technique, together with a ratio of areas between the non-overlapping regions and the overlapping regions of the normalized shapes. The results presented, involving synthetic and real shapes, show that the new normalization approach is much more reliable and robust that the traditional one.