The total ozone and the ozone mixing ratio at various pressure levels in stratosphere measured from the NIMBUS 4 backscattered ultraviolet (BUV) experiment over a 7-year period (1970-1977) comprise a very comprehensive data base available to study the possible effects of solar variability on stratospheric ozone. It is shown that with the decrease in solar activity from 1970 to 1976, the globally averaged ozone inferred from NIMBUS 4 data decreases from about 10-12% in the upper stratosphere to about 1-3% in the lower stratosphere. This systematic decrease at all pressure levels is modulated by a quasi-periodic oscillation of about 2-year period. Both the systematic decrease and the quasi-periodic oscillations in ozone seem to be correlated with the conventional indices of solar activity suggesting a solar UV-ozone relationship. Despite this apparent correlation, it is difficult to account for the observed changes at various pressure levels with our current understanding of the photochemical models and the solar UV flux variations over a solar cycle. The agreement between the observed and the calculated profiles of ozone mixing ratio is considerably improved if the BUV data are corrected for the changes in the instrument sensitivity using Umkehr observations as a reference.