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 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 separate from the first angular sector shuts off the connection between the upstream duct and the downstream duct, - the rotation of the plug according to a third angular sector included in the second angular sector 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, 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 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 separate from the first angular sector shuts off the connection between the upstream duct and the downstream duct, - the rotation of the plug according to a third angular sector included in the second angular sector 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 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 separate from the first angular sector shuts off the connection between the upstream duct and the downstream duct, - the rotation of the plug according to a third angular sector included in the second angular sector 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, to come into contact and actuate the shutter so as to allow a flow from the upstream duct to the purge duct.