The use of proper domain decomposition is shown to have bearing on the computation time in a mode-matching formulation. A simple L-shaped waveguide is taken and is analyzed using mode-matching with two different ways of domain decomposition. In one of the methods, the number of domains is kept minimum so that the analysis is easier, whereas, in the other the motivation is to choose the domains in such a way that all the waveguide wall boundaries are explicitly satisfied. The second way of domain decomposition is shown to be computationally much more efficient as compared to the first one. An L-shaped waveguide with arbitrary chosen dimensions was fabricated and was used to experimentally verify the accuracy of the two ways of domain decomposition. The experimentally and the theoretically obtained numbers match excellently.