The hydraulic machine having axial pistons comprises: a cylinder block mounted to rotate about a first axis of rotation; and a swash plate supporting a sliding disk in rotation about a second axis of rotation which is inclined relative to the first axis of rotation. Coupling rods are connected to the pistons via first spherical joints and to the sliding disk via second spherical joints. For each coupling rod, a synchronization system for providing synchronization between the cylinder block and the sliding disk has two drive surfaces stationary respectively relative to the coupling rod and relative to the sliding disk, the second drive surface being off-center relative to the second spherical joint of the rod, such that a reference amount of clearance between said second drive surface and a first drive surface is small in the zone in which said surfaces come into contact at the time of synchronization in the preferred direction of rotation.
