Linear systems arising from implicit time discretizations and finite difference space discretizations of second-order hyperbolic equations on L-shaped region are considered. We analyse the use of domain deocmposilion preconditioner.s for the solution of linear systems via the preconditioned conjuguate gradient method. For the constant-coefficient sencond-order hyperbolic equations with initial and Dirichlet boundary by , where x is the quotient between the time and steps. Such condition number produces a converage rate that is independent of gridsize and aspect ratios. The result could be extended to parabolic equations.