A system for automatically coordinating a direction of travel with a position of a turret rotatably mounted on an undercarriage of a hydraulic machine including a hydraulic transmission circuit for connecting a main pump to a bi-directional hydraulic travel motor. The circuit includes a travel control distributor able to vary a driving direction of the motor. The system includes a second hydraulic circuit disposed downstream of a pilot pump providing a pilot pressure. The second circuit includes: a valve controller for controlling a direction of travel, activatable by the operator and able to switch the control distributor by sending different command signals; and a reversing valve, interposed between the valve controller and the control distributor. The system further includes a coordination circuit able to switch or maintain the reversing valve according to the position of the turret and to the command signals.