During the solar minimum period of 1954 the cosmic-ray diurnal variation as observed by neutron monitors and muon telescopes underwent a dramatic swing in its direction of maximum intensity, from the normal value between 16:00 and 18:00 local time to as early as 08:00. It is shown that this swing can be explained as being due to a negative radial density gradient of cosmic rays in the inner heliosphere and that this negative gradient is caused by large radial and latitudinal diffusion mean free paths that bring in particles from high latitudes. In principle, such large diffusion mean free paths should simultaneously cause high intensities, as were observed in 1954.