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Aims: We devise a data reduction and calibration system for producing highly-accurate 21-cm H I spectra from the Green Bank Telescope (GBT) of the NRAO. Methods: A theoretical analysis of the all-sky response of the GBT at 21 cm is made, augmented by extensive maps of the far sidelobes. Observations of radio sources and the Moon are made to check the resulting aperture and main beam efficiencies. Results: The all-sky model made for the response of the GBT at 21 cm is used to correct for "stray" 21-cm radiation reaching the receiver through the sidelobes rather than the main beam. This reduces systematic errors in 21-cm measurements by about an order of magnitude, allowing accurate 21-cm H I spectra to be made at about 9' angular resolution with the GBT. At this resolution the procedures discussed here allow for measurement of total integrated Galactic H I line emission, W, with errors of 3 K km s^-1, equivalent to errors in optically thin N_HI of 5 x 10^18 cm^-2., Comment: 49 pages, 25 figures; A&A, in press