The method and the results of an experiment on the study of relativistic _Λ ⁴ H and _Λ ³ H production in interactions of 18 GeV/c⁴He nuclei with CH₂ target nuclei are presented. The experiment was performed using the HYBS-spectrometer. The main registering part of the spectrometer is a (2×0.6×1)m³ streamer chamber placed in a magnetic field of 0.9 T. The streamer chamber was triggered when the beam⁴He nucleus lost one charge unit in the target and then again became double-charged inside the chamber fiducial volume according to the selection criteria for _Λ ^3,4 H hypernucleus production and its mesonic decay with the He nucleus in the final state. After scanning of the pictures, measurements of two-prong events and careful analysis, events of the decays _Λ ⁴ H→⁴He+π^- and _Λ ³ H→³He+π^- were identified. The estimates of the _Λ ⁴ H production cross-section (∼0.4 μb) and its mean lifetime (∼2.2·10^-10s) were obtained. A comparison with the results of other experiments and theoretical calculations is made. By the way, the cross-section of the charge exchange reaction³H+Ne→³He+π^-++...(∼1 mb) was estimated. The work has been performed at the Laboratory of High Energies, JINR, Dubna.