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An experiment in direct registration of neutron nuclei (x≥6x≥6) using a multineutron detector has been conducted for the first time. The results indicate the presence of hexaneutron and/or octaneutron emission in decay of 238238U nuclei. The multineutron detector consisted of 20 3He-filled counters placed in a polyethylene moderator. Samples (emitters) of uranium trioxide (UO3) were used as sources of neutron nuclei. The experiment was conducted for a period of 112.66 days. Thus, the ratios of probabilities of hexaneutron and/or octaneutron emission by the 238238U nuclei to the probabilities of αα-decay have been determined as upper bounds at a 90% confidence level: λ(6n)/λα≤9.3×10−9λ(6n)/λα≤9.3×10−9 and λ(8n)/λα≤3.6×10−10λ(8n)/λα≤3.6×10−10.