The kind of WZ factorizations is the basic mathematics theory for a series of parallel algorithms in solving linear systems. For the symmetric p-tridiagonal matrix, the WZ factorization and its properties were proposed and proved. Furthermore, it also shows that the W-factor of the WZ factorization owns the character that the elements in itare real numbers when the real matrix is symmetric positive definite, and the factorization is unique when the elements in diagonal are positive real numbers.