Shape analysis is utilized across a wide spectrum of scientific fields dealing with large datasets, often comprising 2D images, aiding in the study and decision-making regarding morphology, reconstruction, recognition, and object classification. In this context, the Kendall shape space serves as a common mathematical framework for analyzing and comparing geometric shapes. In this work, by embedding this space into a Euclidean space \(\mathbb R^N\) , we provide a novel characterization thereof, from which we define a new extrinsic sample mean. Having this new mean defined provides a reference point when applying kernel methods based on this embedding.