A valve for controlling the flow rate of a cryogenic fluid in a duct, comprising: - a valve body provided with a plug , the plug having an end to be connected to an actuation system, - an upstream duct , - a downstream duct , - a purge duct provided with a shutter , the upstream duct and the downstream duct opening into the valve body , the purge duct being connected to the upstream duct , and the shutter being configured so as to be, by default, in a shut-off position of the purge duct , the plug being movable in rotation about a longitudinal axis (X-X) in the valve body , so that: - the rotation of the plug according to a first angular sector (A1) defines a flow between the upstream duct and the downstream duct via the valve body , - the rotation of the plug according to a second angular sector (A2) separate from the first angular sector (A1) shuts off the connection between the upstream duct and the downstream duct , - the rotation of the plug according to a third angular sector (A22) included in the second angular sector (A2) actuates the shutter so as to allow a flow from the upstream duct to the purge duct , - the downstream duct being opposite said end of the plug on said axis (X-X) and the plug having a lug arranged on an outer surface of the plug , the lug being configured, when the plug is driven in rotation in the third angular sector (A22), to come into contact and actuate the shutter so as to allow a flow from the upstream duct to the purge duct . - a valve body provided with a plug , the plug having an end to be connected to an actuation system, - an upstream duct , - a downstream duct , - a purge duct provided with a shutter , the upstream duct and the downstream duct opening into the valve body , the purge duct being connected to the upstream duct , and the shutter being configured so as to be, by default, in a shut-off position of the purge duct , the plug being movable in rotation about a longitudinal axis (X-X) in the valve body , so that: - the rotation of the plug according to a first angular sector (A1) defines a flow between the upstream duct and the downstream duct via the valve body , - the rotation of the plug according to a second angular sector (A2) separate from the first angular sector (A1) shuts off the connection between the upstream duct and the downstream duct , - the rotation of the plug according to a third angular sector (A22) included in the second angular sector (A2) actuates the shutter so as to allow a flow from the upstream duct to the purge duct , - the downstream duct being opposite said end of the plug on said axis (X-X) and - the rotation of the plug according to a first angular sector (A1) defines a flow between the upstream duct and the downstream duct via the valve body , - the rotation of the plug according to a second angular sector (A2) separate from the first angular sector (A1) shuts off the connection between the upstream duct and the downstream duct , - the rotation of the plug according to a third angular sector (A22) included in the second angular sector (A2) actuates the shutter so as to allow a flow from the upstream duct to the purge duct , - the downstream duct being opposite said end of the plug on said axis (X-X) and the plug having a lug arranged on an outer surface of the plug , the lug being configured, when the plug is driven in rotation in the third angular sector (A22), to come into contact and actuate the shutter so as to allow a flow from the upstream duct to the purge duct . <EOS>