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For the first time, ultracold neutrons have been stored in a volume formed of foils coated with diamond-like carbon. The coefficients for loss, η, and depolarization, β, per wall collision were determined simultaneously. The results for different samples, η∼10−4 and β∼10−5–10−6, are among the best values measured for high Fermi potential materials without elaborate surface pre-treatment. Thin foil storage material will be widely applicable, e.g., in neutron β-decay studies.