The formation of luminescent subordinate He I lines by the absorption of radiation from a source in lines of the main He I series in an expanding Universe is considered. A burst of radiation in continuum is assumed to occur at some instant of time corresponding to redshift z₀. This radiation is partially absorbed at different z < z₀ in lines of the main He I series (different pumping channels) and then is partially converted into radiation in subordinate lines. If ν_ik is the laboratory transition frequency of some subordinate line emerging at some z, then at the present epoch its frequency will be ν = ν_ik/(1 + z). The quantum yield, i.e., the number of photons emitted in the subordinate line per initial excited atom, has been calculated for different z (and, consequently, for different ν). Several pumping channels have been considered. We show that the luminescent lines can be both emission and absorption ones; the same line can be an emission one for one of the pumping channels and an absorption one for another. For example, the 1s2s–1s2p (1S–1P*) line is an emission one for the 1s2–1s2p pumping and an absorption one for the 1s2–1s3p pumping. We show that in the frequency range 30–80 GHz the total quantum yield for the first and second of the above channels can reach +50 and −50%, respectively.