The invention relates to a Francis runner (200) for a hydraulic machine, comprising: a wheel (1), which is rotationally symmetrical about an axis of rotation (Z) of the runner (200); a crown (12); and a plurality of inwardly curved vanes (21), each of which has a peripheral edge (212). The peripheral edge (212) of at least one of the vanes is curved, the concavity thereof facing toward the outside of the runner (200). The maximum value of the distance measured between any point on the peripheral edge (202) and a straight line passing through a first connection point between the peripheral edge (212) and the wheel (1), and through a second connection point between the peripheral edge (212) and the crown (12), is at an intermediate point on the peripheral edge (212). The radius (Rn) from the intermediate point (N) is strictly smaller than the radius (Ra) from the first connection point (A). The radius (Rn) from the intermediate point (N) is strictly smaller than the radius (Rc) from the second connection point (C).