The problem of minimizing the number of L-shaped channels in the routing region definition and ordering for building-block layouts is studied. Given a building-block layout of rectangular modules, the routing region is to be decomposed into straight and L-shaped channels and routed in a certain order. Since channel routers usually produce superior results, it is desirable to minimize the number of L-shaped channels used in such a decomposition. A fast algorithm that can produce provably better results than a previously proposed algorithm is presented. This algorithm is based on a study of the structure of such layouts, and a transformation of the original problem to a graph theoretical problem. For examples of up to 136 channels, the algorithm took less than one-tenth of a second to finish the computation, and it obtained up to 29% reduction in the number of L-shaped channels over the results produced by another algorithm.