Studies have been done on the variability of cosmic rays flux during solar quiet days at mid and high latitudes. By using the 5 quietest days for each month, the monthly mean diurnal variation of cosmic ray anisotropy have been derived for the period 1981 to 2007, which covers part of cycles 21, 22 and 23. These quiet days are days during which the sun is relatively magnetically quiet, leading to less anisotropic behaviour in the diurnal flux of cosmic rays measured on the earth surface. Four stations (Rome, Oulu, Inuvik and Thule) were used in this study to understand the important features of the high latitude and mid-latitude diurnal wave, and how solar and geomagnetic activity may be influencing the wave characteristics. Cosmic ray wave characteristics were obtained by discrete Fourier transform (DFT). The mean, diurnal amplitude, phase and dispersion for each month's diurnal wave were calculated and profiled. There was clear indication that the terrestrial effect on the variability of the monthly mean of Cosmic ray count rates was more associated with geomagnetic activity rather than rigidity of the cosmic rays. Correlation of the time series of these wave characteristics (that is, amplitude and phase) with solar and geomagnetic activity index showed better association with solar activity.