A propagation matrix method for the solution of the parabolic equation in ocean acoustics is presented, where the sound fields at an arbitrary distance are expressed as a product of the initial fields and a sequential multiplication of the propagation matrices. The method contains two main calculation steps, i.e., producing and multiplying the propagation matrices. The first step allows a two-level parallel algorithm. In the second step an eigenvalue decomposition technique is developed to improve the efficiency in the case of a range-independent waveguide. The efficiency of the parallelized algorithm shall be tested in the future.