We solve the one-loop Renormalization Group Equations (RGE) and show that each of the Quark Yukawa Couplings (QYC) matrices for the up and down quarks depends on two functions of energy. The energy dependence is such that the diagonalizing matrices of the up QYC and the ratiomc/muare constant while for the down QYC the diagonalizing matrices are energy dependent. From this it follows that the evolution of the CKM matrix depends on energy through one known function. ©1999 American Institute of Physics.