The differential rain attenuation is considered to be one of the main propagation factors causing interference between adjacent Earth-Space paths. In the present paper, an existing method to predict the differential rain attenuation statistics is properly modified to include a more complicated but accurate estimation of the slant path lengths affected by the rain medium. The modified method is oriented to be generally applicable, particularly in the case of satellite paths operating under low elevation angles in the Ku-band, where the accurate estimation of the effective slant path lengths is very critical. The present results are compared with a set of available simulated data for the differential attenuation over pairs of paths located in Montreal. The influence of various other parameters such as the geographic latitude and climatic zone is also examined.