The correlation coefficient of the two horizontal components of strong ground motion is studied as an aid in specifying characteristics of synthetically generated motions to be used simultaneously in the dynamic response of structures. The recorded available data is “extended” by recognizing certain properties of the components of ground motion such that the statistical data used includes all possibilities of the orientation of recording accelerographs. The probability density function of the correlation coefficients is derived numerically, which could be used for further studies of the characteristics of ground motion. From this distribution, an approximate yet simple description of the correlation coefficient of the components of ground motion is derived for use in seismic design codes: it is shown that the value of the correlation coefficient of the components of ground motion can be approximated by a rectangular distribution ranging from −0.32 to 0.32. For all practical purposes the correlation coefficient varies from −0.5 to +0.5.