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For special structured linear systems, WZ factorizations of matrices are basic mathematical theories to design a class of parallel solving algorithms. So, firstly, new WZ factorizations for the p-tridiagonal matrix are proposed and proved. Next, an effective parallel algorithm is designed. Solving both the subsystem in each processor and the reduced subsystem makes use of the WZ factorization so that a two-level method is formed. The experiment results confirm the validity of our method.