A general distribution function q (t) W/m2for clear days is suggested to predict the global solar irradiance incident on a horizontal surface as a function of the local day time and the maximum daily value of the incident solar irradiance qmax. Moreover, the authors suggested a form to express qmaxin terms of the solar constant. The value of the solar constant is also adjusted to its variation with the distance between earth and the sun. This is done to get a complete theoretical expression for q (t) rather than semi- empirical formulae introduced in previous trials. Comparison between the computed values according to the introduced theoretical formula of q (t) and the corresponding published experimental data recorded in Barcelona(Spain) , Hong Kong (China), Cairo(Egypt), Makkah ,Jeddah(Saudi Arabia) is made.Good fitting is obtained except for few extreme points.