The perspective a non-cryogenic technology for an extraction of helium from a natural gas in a membrane installation operating in a non-stationary mode is considered. A separating membrane in this installation is in the form of a closed microsphere. A microscopic size of the walls of the capsules provides a high rate of diffusion of the gases unattainable in the systems with a stationary mode. It was developed a wave method for calculating of the membrane systems with a non-stationary mode. The calculation is carried out by a decomposition of the input concentration signal in the Fourier series for natural frequencies of a periodic process. At the same time each of their own concentration waves, independently of the others, pass through the layer of microcapsules. At the output all the solutions for the separate own waves are summarized. On a concrete example of the helium extraction from a natural gas the possibilities of a new technology of the helium extraction is demonstrated. It has been shown that passing of the natural gas through the installation with three apparatuses 10 m long filled in cenospheres allows to achieve an extraction of helium of 33 % helium.