The concept of L-shaped channels was introduced to generate a feasible routing order for nonslicing structure placement in the building-block layout design. This thesis presents and algorithm for routing the 2-layer gridless L-shaped channels in the manhattan model. The L-shaped channel is divided into three regions, a switchbox having floating terminals in the two adjacent sides and two 3-side channels. The switchbox is routed first, then the positions of the floating terminals are determined. The 3-side channels are routed by the well-known channel router, YACR 2, which is specially modifed to handle fixed terminals on the third side. This algotithm is implemented in C and the performance is analyzed by exprimenting on the randomly generated data. The experimental results show that most data can be routed within the number of tracks less than 110\% of their densities.