A vacuum pump for a motor vehicle engine which has a stator and a chamber, has a side wall, and the side wall has a transversal section with a predetermined shape. The rotor mounted in the chamber is capable of rotating around a rotation axis parallel to the side wall. The vane mounted on the rotor is free to slide in a direction at right angles with respect to the rotation axis of the rotor, and the vane has a predetermined length and two opposite end portions that substantially slide along the side wall of the chamber. At least one of the end portions of the vane has at least one part that has a bend radius substantially equal to that of a part of the side wall, when the one vane is at a reference operating position.