Context : 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 \times 10 ^ { 18 } cm ^ { -2 } . Conclusions :