A hydraulic pump comprises at least one alternating-cycle piston (20) having a suction phase and a delivery phase, and sliding in a fixed cylinder (22). The pump possesses in addition a nonreturn suction valve (32) placed between a source of fluid under low pressure (28) and a working chamber (30) defined in the cylinder, and a nonreturn delivery valve (34) placed between the working chamber (30) and an output chamber (16) for the fluid under high pressure, connected to an application circuit 10, 12). The output chamber (16) possesses a wall (40) which is movable as a function of the pressure which prevails in the output chamber (16), the movable wall (40) being capable of controlling the locking of the delivery valve (34) in an open position substantially during the greater part of the suction phase when the pressure in the output chamber (16) is greater than a given pressure, in such a way that the suction valve (32) stays closed in a corresponding manner.