Nearly 6 years of global ozone monthly mean data from the Nimbus 4 BUV instrument are compared with monthly values of solar activity using 10.7-cm flux (F(10.7)) as a parameter. Several techniques are explored in calculating the correlation between the two data sets, and all yield relatively high correlations, ranging from R = 0.68 for 'raw' monthly means to 0.94 using a 6-month running mean for each data set. It is shown, however, that the bulk of the correlation is due to the long-term decreasing trends in both data sets. When the long-term trends are removed, a cross-correlation analysis produces a maximum with no phase shift or with the ozone variations leading the solar variations by 1 month, thus reducing the likelihood of a cause and effect relationship on time scales of this order. Considering the current uncertainty in the long-term stability of the BUV instrument, and the resulting uncertainty in any long-term trend derived from its data, it is unrealistic to draw firm conclusions about a solar cycle influence on total ozone from this satellite data set.