An experiment is carried out to analyze the mechanism of excitation of atomic hydrogen in a helium plasma, the hydrogen content being insignificant for the kinetics of excited and ionized helium. The intensities of the atomic helium and hydrogen spectral lines (H_α and H_β) are measured, and densities of He(2³S₁) and He(2¹S₀)metastable atoms and of He₂(a³ Σ⁺ _u) metastable molecules are examined in a decaying plasma with pulsed heating of electrons using the absorption and laser-induced fluorescence techniques, respectively. It is shown that excitation of the (H_α and H_β) lines in a decaying plasma occurs due to excitation transfer He₂[a³ Σ⁺ _u] + H₂ → He + He(n>2) +H, which involves metastable states of molecular helium as the energy donor.