Solving the linear system Ax = b is an active area of research in engineering. Many researchers have applied preconditioners to the linear system Ax = b. In this work, we introduce two new preconditioners for solving linear systems. The best property of the introduced preconditioners is that they can be used under weaker conditions than the previous preconditioners in the literature. We propose preconditioned associated accelerated overrelaxation (AOR) iterative methods with these two new preconditioners, and give the corresponding convergence results. Numerical examples show an improvement in the convergence rate of the AOR preconditioned iterative matrices.