Method for processing a stream of LNG obtained by cooling using a first refrigeration cycle, the method being of the type comprising the following steps: (a) the stream of LNG which has been brought to a temperature of less than -100°C is introduced into a first heat-exchanger; (b) the stream of LNG is sub-cooled in the first heat-exchanger by heat-exchange with a refrigerating fluid in order to form a stream of sub-cooled LNG; and (c) the refrigerating fluid is subjected to a second semi-open refrigeration cycle which is independent of the first cycle, the method comprising the following steps: (d) the stream of sub-cooled LNG is expanded in a dynamic manner in an intermediate turbine, maintaining this stream substantially in the liquid state; (e) the stream from the intermediate turbine is cooled and expanded and then introduced into a distillation column; (f) a stream of denitrogenated LNG at the bottom of the column and a stream of gas at the top of the column are recovered; and (g) the top stream of gas is compressed in a stage compressor, and, at an intermediate pressure stage of the compressor, a first portion of the top stream of gas which is brought to an intermediate pressure PI is extracted in order to form a stream of combustible gas; the second refrigeration cycle comprising the following steps: (i) an initial stream of refrigerating fluid is formed from a second portion of the top gas which has been compressed at the intermediate pressure PI; (ii) the initial stream of refrigerating fluid is compressed to a high pressure PH which is greater than the intermediate pressure PI in order to form a stream of compressed refrigerating fluid; (iii) the stream of compressed refrigerating fluid is cooled in a second heat-exchanger; (iv) the stream of compressed refrigerating fluid from the second heat-exchanger is separated into a main cooling stream and a sub-cooling stream of the LNG; (v) the sub-cooling stream is cooled in a third heat-exchanger, then in the first heat-exchanger; (vi) the sub-cooling stream from the first heat-exchanger is expanded to a low pressure PB which is lower than the intermediate pressure PI in order to form a substantially liquid sub-cooling stream of the LNG; (vii) the substantially liquid sub-cooling stream is evaporated in the first heat-exchanger in order to form a reheated sub-cooling stream; (viii) the main cooling stream is expanded substantially to the low pressure PB in a main turbine and the cooling stream from the main turbine is mixed with the reheated sub-cooling stream in order to form a mixed stream; (ix) the mixed stream is reheated successively in the third heat-exchanger, then in the second heat-exchanger in order to form a reheated mixed stream; and (x) the reheated mixed stream is introduced into the compressor at a low pressure stage located upstream of the intermediate pressure stage. (a) the stream of LNG which has been brought to a temperature of less than -100°C is introduced into a first heat-exchanger; (b) the stream of LNG is sub-cooled in the first heat-exchanger by heat-exchange with a refrigerating fluid in order to form a stream of sub-cooled LNG; and (c) the refrigerating fluid is subjected to a second semi-open refrigeration cycle which is independent of the first cycle, (d) the stream of sub-cooled LNG is expanded in a dynamic manner in an intermediate turbine, maintaining this stream substantially in the liquid state; (e) the stream from the intermediate turbine is cooled and expanded and then introduced into a distillation column; (f) a stream of denitrogenated LNG at the bottom of the column and a stream of gas at the top of the column are recovered; and (g) the top stream of gas is compressed in a stage compressor, and, at an intermediate pressure stage of the compressor, a first portion of the top stream of gas which is brought to an intermediate pressure PI is extracted in order to form a stream of combustible gas; (i) an initial stream of refrigerating fluid is formed from a second portion of the top gas which has been compressed at the intermediate pressure PI; (ii) the initial stream of refrigerating fluid is compressed to a high pressure PH which is greater than the intermediate pressure PI in order to form a stream of compressed refrigerating fluid; (iii) the stream of compressed refrigerating fluid is cooled in a second heat-exchanger; (iv) the stream of compressed refrigerating fluid from the second heat-exchanger is separated into a main cooling stream and a sub-cooling stream of the LNG; (v) the sub-cooling stream is cooled in a third heat-exchanger, then in the first heat-exchanger; (vi) the sub-cooling stream from the first heat-exchanger is expanded to a low pressure PB which is lower than the intermediate pressure PI in order to form a substantially liquid sub-cooling stream of the LNG; (vii) the substantially liquid sub-cooling stream is evaporated in the first heat-exchanger in order to form a reheated sub-cooling stream; (viii) the main cooling stream is expanded substantially to the low pressure PB in a main turbine and the cooling stream from the main turbine is mixed with the reheated sub-cooling stream in order to form a mixed stream; (ix) the mixed stream is reheated successively in the third heat-exchanger, then in the second heat-exchanger in order to form a reheated mixed stream; and (x) the reheated mixed stream is introduced into the compressor at a low pressure stage located upstream of the intermediate pressure stage.