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Results are presented on the ratio of neutron and proton structure functions, F~'/F~, deduced from deep inelastic scattering of muons from hydrogen and deuterium. The data, which were obtained at the CERN muon beam at 90 and 280 GeV incident energy, cover the kinematic range x = 0.002-0.80 and Q2 = 0.1-190 GeV2. The measured structure function ratios have small statistical and systematic errors, particularly at small and intermediate x. The observed Q2 dependence in the range x = 0.1-0.4 is stronger than predicted by perturbative QCD. From the present data together with results from other experiments it is suggested that the twist-four coefficient for the proton is smaller than that for the neutron for x larger than 0.2.