Today, especially in metropolitan cities, there is a traffic problem caused by roads and the number of vehicles. Especially since the construction in the city is over, there are measures such as building bridges and opening roads from below are taken to solve this problem. This solution is only an artificial solution to reduce traffic for a certain period of time. Based on this problem, it is aimed to make road design at the beginning of urbanization and to analyze the situation of two-way one-way roads in the name of not to encounter such a problem in the new settlements to be established or to change the routes of the roads in certain cities if they can be arranged. In this study were used quantitative research method and experimental design. Within the scope of the study, symmetric groups, permutation function and its combination were utilized. Let n be the length of a permutation function written as a circle. The symmetric group in which this function is located is Sn, and a method has been developed that can be written as the composite of functions of the same length and less than this length in this group. Thanks to this method, a permutation function was created for the roads to be determined according to the important centers in a settlement, the circular software and length of the permutation function were found, and the road routes between these centers could be written as a composite of permutation functions with less length in circular representation, and accordingly, road designs could be made. For each road design, cost calculation, accessibility to other centers, one-way and two-way road conditions were examined and alternatives were revealed. Based on this study, algorithms and software of the road designs developed can be developed and new urbanization and settlement planning can be made accordingly. Keywords: Permutation, composition, graph theory, path design, number theory