Method for the liquefaction of nitrogen using the recovery of cold energy deriving from the evaporation of liquefied natural gas comprising the steps of: sending a flow of nitrogen gas to a first and a second stage of the high pressure recirculation compressor; sending the flow of nitrogen exiting said second stage of the compressor to a liquefaction heat exchanger; sending to said liquefaction heat exchanger a flow of liquefied natural gas, countercurrent to the flow of nitrogen exiting said compressor; sending a portion of the flow of liquid nitrogen exiting said liquefaction heat exchanger to an expander; sending the flow of nitrogen exiting said expander to a medium pressure separator that delivers an exiting flow of liquefied nitrogen; characterized in that the flow of nitrogen to be liquefied is sent to a precooler; the flow exiting from said precooler is sent to a collector that delivers the flow of nitrogen gas that is send to the first and the second stage of the compressor; wherein sending the flow of nitrogen gas to the first and the second stage of the compressor comprises: sending the flow of nitrogen gas to a heat exchanger of the high pressure recirculation compressor; sending the flow of nitrogen exiting said heat exchanger of the high pressure recirculation compressor to the first stage of the high pressure recirculation compressor; the compressed flow exiting said first stage is sent to the heat exchanger of the high pressure recirculation compressor and the flow exiting this heat exchanger is sent to the second stage of the high pressure recirculation compressor at -150°C; and in that the remaining portion of the flow of liquid nitrogen exiting said liquefaction heat exchanger is sent first to said heat exchanger of the high pressure recirculation compressor countercurrent to said flow of nitrogen gas and to said compressed flow of nitrogen exiting said first stage of the compressor; then to said precooler countercurrent to said flow of nitrogen to be liquefied and then to a turbine; sending the flow exiting from said turbine to said collector that combines the flow exiting from the turbine and the flow exiting from the precooler to produce said flow of nitrogen sent to the first and second stage of the compressor. sending a flow of nitrogen gas to a first and a second stage of the high pressure recirculation compressor; sending the flow of nitrogen exiting said second stage of the compressor to a liquefaction heat exchanger; sending to said liquefaction heat exchanger a flow of liquefied natural gas, countercurrent to the flow of nitrogen exiting said compressor; sending a portion of the flow of liquid nitrogen exiting said liquefaction heat exchanger to an expander; sending the flow of nitrogen exiting said expander to a medium pressure separator that delivers an exiting flow of liquefied nitrogen; characterized in that the flow of nitrogen to be liquefied is sent to a precooler; the flow exiting from said precooler is sent to a collector that delivers the flow of nitrogen gas that is send to the first and the second stage of the compressor; wherein sending the flow of nitrogen gas to the first and the second stage of the compressor comprises: sending the flow of nitrogen gas to a heat exchanger of the high pressure recirculation compressor; sending the flow of nitrogen exiting said heat exchanger of the high pressure recirculation compressor to the first stage of the high pressure recirculation compressor; the compressed flow exiting said first stage is sent to the heat exchanger of the high pressure recirculation compressor and the flow exiting this heat exchanger is sent to the second stage of the high pressure recirculation compressor at -150°C; and in that the remaining portion of the flow of liquid nitrogen exiting said liquefaction heat exchanger is sent first to said heat exchanger of the high pressure recirculation compressor countercurrent to said flow of nitrogen gas and to said compressed flow of nitrogen exiting said first stage of the compressor; then to said precooler countercurrent to said flow of nitrogen to be liquefied and then to a turbine; sending the flow exiting from said turbine to said collector that combines the flow exiting from the turbine and the flow exiting from the precooler to produce said flow of nitrogen sent to the first and second stage of the compressor. sending the flow of nitrogen gas to a heat exchanger of the high pressure recirculation compressor; sending the flow of nitrogen exiting said heat exchanger of the high pressure recirculation compressor to the first stage of the high pressure recirculation compressor; the compressed flow exiting said first stage is sent to the heat exchanger of the high pressure recirculation compressor and the flow exiting this heat exchanger is sent to the second stage of the high pressure recirculation compressor at -150°C; and in that the remaining portion of the flow of liquid nitrogen exiting said liquefaction heat exchanger is sent first to said heat exchanger of the high pressure recirculation compressor countercurrent to said flow of nitrogen gas and to said compressed flow of nitrogen exiting said first stage of the compressor; then to said precooler countercurrent to said flow of nitrogen to be liquefied and then to a turbine; sending the flow exiting from said turbine to said collector that combines the flow exiting from the turbine and the flow exiting from the precooler to produce said flow of nitrogen sent to the first and second stage of the compressor.