A hydraulic machine, in particular a hydraulic motor, comprising: a casing (1); a piston (4) which can slide in the casing, the piston separating two chambers (8, 9); hydraulic switching means (C) for supplying liquid to and for evacuating the chambers separated by the piston, comprising at least one connecting rod (14) acting on a distribution member which can adopt two stable positions; and initiating means comprising a pusher (18) which, at the end of the piston stroke, can cause a sudden change in the position of the switching means, under the action of an elastic means (E), in order to reverse the stroke. The elastic means (E) is secured, at each of its ends, to an articulation member (20a, 20b) respectively accommodated in a housing (21, 22) provided on the connecting rod and on another moving part (18) of the machine, each housing (21, 22) being open in a direction substantially opposed to the direction of the force exerted by the elastic means (E) in the housing, such that each articulation member (20a, 20b) can be removed from its open housing (21, 22) against the action of said force, thereby simplifying assembly and disassembly.