The authors describe the process for modernizing the existing liquefier with minimum alteration of its cooling block, that liquefier being helium expansion-type liquefier G-3, made at the Institute of Physical Problems, Academy of Sciences of the USSR, which operates at a stable output of 40 liters/h. A nitrogen tank and a pistontype expander in the preliminary cooling stages and a throttle in the liquefaction stages are used in G-3. Improving the efficiency of such a cooling cycle is limited by the fact that the optimal parameters of throttle stage of liquefaction do not match with the optimal parameters of the expander in the preliminary cooling stages. Thus, for improving cycle efficiency the pressure in the preliminary stages must be increased but reduced in the liquefaction stage. This paper also presents the solution to this problem. It is further demonstrated that the use of vapor-liquid expander in the liquefaction stage of helium cooling cycle helps increase the output of the unit by 40% in a relatively simple way.