In recent Printed Circuit Boards (PCB), the design size and density have increased, and the improvement of routing tools for PCB is required. There are several routing tools which generate high quality routing patterns when connection requirement can be realized by horizontal and vertical segments only. However, in high density PCB, the connection requirements cannot be realized when only horizontal and vertical segments are used. Up to one third nets can not be realized if no non-orthogonal segments are used. In this paper, a routing method for a single-layer routing area that handles higher density designs in which 45-degree segments are used locally to relax the routing density is introduced. In the proposed method, critical zones in which non-orthogonal segments are required in order to realize the connection requirements are extracted, and 45-degree segments are used only in these zones. By extracting minimal critical zones, the other area that can be used to improve the quality of routing pattern without worry about connectivity issues is maximized. Our proposed method can utilize the routing methods which generate high quality routing pattern even if they only handle horizontal and vertical segments as subroutines. Experiments show that the proposed method analyzes a routing problem properly, and that the routing is realized by using 45-degree segments effectively.