Context. CMEs can effect the distribution of dust grains in the corona. The brightness of the visible F corona is expected therefore to change as the frequency of CMEs varies with solar cycle. Aims. We search for a variation in the F corona by comparing LASCO C2 observations from solar minimum and maximum.Methods. An established inversion method is used to calculate the visible F corona brightness from LASCO C2 solar minimum observations made during 1996/10. Good agreement is found with the F corona brightness calculated from Skylab observations during 1973/05-1974/02 for heights of 3-6 R . The unpolarized brightness, which is dominated by the unpolarized F corona brightness at these heights, is obtained by subtracting many pairs of polarized brightness images from total brightness images and averaging over a solar rotation. We calculate the unpolarized brightness for both solar activity minimum and maximum. Results. The unpolarized brightness, and therefore the F corona, remain virtually unchanged between solar minimum and maximum at heights above 2.6 R , despite the large change in the shape and activity of the corona. Using a simple density model, it is shown that the small variation in unpolarized brightness seen below 2.6 R can arise from differences in the distribution of electron density, and therefore cannot be attributed to a variation in the F corona. Conclusions. Despite the large rise in frequency of CMEs from solar minimum to maximum, the F coronal brightness, at heights of 3-6 R in the visible, remains very stable.