Abstract: Administrative units are often distinguished by using different colors in cartography. Based on Heawood Theorem and its proving steps, this paper forwards a method in which administrative units may be automatically colored in given number of colors by adjusting some colored units. This coloring process can color any administrative units without separated areas in at most five colors. In addition, color weights are introduced in this process to meet the requirement of balancing different color areas no a map. By analysing graphic features of adminostrative units and earto graphic requiremts, this paper finally points out that no available process can assign given number of colors for any administrative units with separted areas so that any two neighbor units have different colors.