A novel approach to fitting parabolas to scattered data is introduced by putting special emphasis on the robustness of the approach. The robust fit is achieved by not taking into account a proportion of the “most outlying” observations, allowing the procedure to trim them off. The most outlying observations are self-determined by the data. Procrustes analysis techniques and a particular type of “concentration” steps are the keystone of the proposed methodology. An application to a retinographic study is also presented.