The one loop Renormalization Group Equations for the Yukawa couplings of quarks are solved. From the solution we find the explicit energy dependence ont=ln&hthinsp;E/&mgr;of the evolution of thedownquark massesq=d,s,bfrom the grand unification scale down to the top quark massmt.These results together with the earlier published evolution of theupquark masses completes the pattern of the evolution of the quark masses. We also find the energy dependence of the absolute values of the Cabibbo-Kobayashi-Maskawa (CKM) matrix|Vij|.The interesting property of the evolution of the CKM matrix and the ratios of the quark masses:mu,c/mtandmd,s/mbis that they all depend ontthrough only one function of energyh(t).©2001 American Institute of Physics.