We have extended our earlier study of the cosmic ray diurnal anisotropy at high primary rigidities to cover the 1980-1987 period. The median primary rigidity of response (R(m)) of the detectors which provide data for our study covers a wide range, 16 GV less-than-or-equal-to R(m) less-than-or-equal-to 331 GV. Our analyses now encompass a complete solar magnetic cycle. The computed values of the limiting primary rigidity (R(c)) for the period vary over a wide range (30 GV less-than-or-equal-to R(c) less-than-or-equal-to 200 GV). The regime of the East-West anisotropy is re-established after 1980. However, we have uncovered several new details which are different. For the 1965-1980 period, the mean value of the amplitude of the anisotropy is 0.5%. The amplitude of the diurnal anisotropy for 1965 and 1986-1987 is about 20% smaller. Very large amplitudes of diurnal variation are observed during the 1982-1985 period, at all primary rigidities. This is quite unlike our prior experience, with similar data, for the 1965-1979 period. We have computed the values of the coupled variable lambda(parallel-to)G(r) for the two solar magnetic polarity epochs. We find that its value for qA < 0 epochs remains constant at about 1%, independent of the primary rigidity. For qA > 0 epochs, its value is significantly lower. We argue that the ratio lambda(perpendicular-to)/lambda(parallel-to) has a mean value of about 1/10, for the solar magnetic cycle. We confirm that the contribution of ''drift'' terms to diurnal anisotropy is small but finite.