Motivated by the structure of a matrix factorization introduced recently by Evans (1999), we introduce a new WZ factorization for use with the partition method for parallel solution of tridiagonal systems. The factorization helps us to uncouple partitioned subsystems for parallel processing of their solution. A crucial question for the validity of the partition method is the existence and stability of the whole solution across the partitioning blocks . We show that if the given system is nonsingular and diagonally dominant, then within each block the WZ factorization exists and is (numerically) strongly stable, and the solution across the partitioning blocks exists (does not terminate prematurely).