A hydraulic machine comprising a drum (12) rotated by an input shaft, comprising cylinders (14) distributed around the shaft, each receiving a piston that slides on the basis of the rotation of the shaft, each cylinder opening at an opening (30) on a transverse face of the drum bearing on a plate having inlet and outlet manifolds, the openings (30) comprising, relative to the cylinders (14) of same, angular offsets comprised within a total offset range, characterized in that the offsets of the openings (30) are disposed at one end or the other of this offset range.