The Magnetic Pileup Boundary (MPB) is a sharp and permanent plasma boundary located between the bow shock and the ionospheric boundary, reported so far at Mars and comets. We use Mars Global Surveyor Magnetometer data to do a quantitative analysis of the magnetic field geometry in the surroundings of the Martian MPB. As a result, we report for the first time a dramatic enhancement of the magnetic field draping at this boundary. This new feature, already reported at comets, is independent of the presence of the crustal magnetic sources. Comparisons with similar results across the Martian and cometary magnetotails reveal that the MPB and the magnetotail boundary are connected. Moreover, the study of this feature can help understand the physics of the Venusian magnetic barrier.