NOVELTY - Nitrogen (1) is compressed to a supercritical pressure, cooled by heat exchange with a flow of liquefied natural gas (LNG)(15) in a first exchanger (3), expanded to a first pressure and at least partially liquefied. Only part of the LNG sent to the first exchanger vaporizes in the first exchanger.    USE - Producing liquefied nitrogen using LNG as the coolant    ADVANTAGE - Only a small fraction of the LNG vaporizes in the first exchanger    DETAILED DESCRIPTION - Part of the LNG leaves the first exchanger in gaseous form through a first outlet and the rest leaves in liquid form upstream of the first outlet. Less than 10% of the LNG vaporizes in the first exchanger. Part of the LNG is sent to an intermediate point in the first exchanger and leaves in gaseous form and the rest is sent to the cold end of the exchanger and leaves the intermediate point in liquid form. The nitrogen which is heated in the first exchanger is mixed with the nitrogen to be compressed and/or is compressed to a pressure below supercritical. The liquefied nitrogen (6) is super-cooled in a second exchanger and divided into two parts. One part is expanded in a valve (45) to a second pressure lower than the first pressure to form a two-phase mixture which is sent to a phase separator (50) and the liquid fraction super-cools the liquefied nitrogen in the second exchanger, and the other part is the produced liquid nitrogen. The gaseous fraction from the phase separator is reheated and mixed with the nitrogen to be liquefied. Part of the liquefied nitrogen (10) is expanded to a second pressure lower than the first pressure, partially vaporized and the vaporized part is sent to the first exchanger. Part of the expanded nitrogen (5) in gaseous form is reheated in the first exchanger before being mixed with the nitrogen to be liquefied upstream of the first exchanger. Device for carrying out this process with means of sending a nitrogen flow and a LNG flow to a first exchanger, means for isenthalpic expansion of the nitrogen cooled in the first exchanger to form a liquid and a gaseous fraction and means of sending the liquid nitrogen to storage. The device includes means (18) for extracting part of the LNG from the first exchanger in gaseous form and means (16, 17) of extracting part of the LNG from the first exchanger in liquid form.    DESCRIPTION OF DRAWING(S) - Schematic showing process    Nitrogen (1)    First exchanger (3)    Expanded nitrogen (5)    Liquefied nitrogen (10)    LNG (15)    Means of extracting liquid LNG from first exchanger (16)    Means of extracting LNG from first exchanger (17)    Means of extracting gaseous LNG from first exchanger (18)    Phase separator (50)