A direct parallel method called Alternate Quadrant Interlocking Factorization (AQIF);A=WZ, is introduced (Rao,Parallel Algorithms and Applications,4, 1-20, 1994) for the general solution of the linear systemAx=b. The matricesWandZare closed under multiplication and inversion. In this paper AQIF is used with partition method for the solution of the banded linear system. The AQIF of the coefficient matrix in each block has the properties that when A is banded with the semibandwidth β, the space generated byei, en−I+11≤i≤β, is invariant under the transformationW, so is invariant under the transformationW−1, whereejdenotesndimensional unit vector with I injth position and 0's elsewhere and the solution process with the coefficient matrixZproceeds from the first and last unknowns towards middle ones. These properties of AQIF help us to decouple the partitioned systems for the parallel execution once ‘reduced system’ is solved.