Abstract A re-examination of cosmic ray data at the 1954 solar minimum shows that the anomalous diurnal variation during July, August and September 1954 was not a sidereal time effect but was associated with a streaming of cosmic rays in a direction perpendicular to the interplanetary field lines and towards the sun. The best estimate of the amplitude of the variation was δI/ I = (3.9 ± 0.3) × 10 −3, independent of rigidity P for P ≤ P m ∼ 30 GV and zero at higher rigidities. The asymptotic direction of the maximum made an angle of (53 ± 6)° with the Sun-Earth line. The phenomenon is discussed in terms of the theory of diffusion and scattering of cosmic rays in the interplanetary medium. It is shown that the phenomenon could have been the result of an additional gradient in cosmic ray density due to asymmetric modulation of cosmic rays north and south of the ecliptic plane. Assuming that the interplanetary field was predominantly directed towards the Sun the effect implied a shift of the effective minimum of cosmic ray density by some 15° northwards from the ecliptic. It is surmised that this asymmetric modulation may have some connection with the asymmetry in solar activity at the 1964–1965 solar minimum. Reasons are given for supposing that such ‘reverse streaming’ of cosmic rays is likely to occur only close to solar minima.