The multi-beam array stitching test system (MASTS) based on the Hartmann principle is employed to measure the aberrations in large-aperture optical systems. As each small-aperture and ideal parallel beam traverses the optical system, it is converged into a spot at the focal plane of the optical system. The centroid position of the spot contains the information about the wavefront slope of the sub-aperture at that specific location in the optical system. Scanning the optical system with this small-aperture beam across the entire aperture of the optical system, we can yield the aberration information to be tested. To mitigate pointing errors induced by scanning motion and accurately obtain the aberration signals of the optical system, nine beams are integrated into a 3 x 3 multi-beam array system, and their directions are aligned to be identical. However, achieving complete alignment in the same direction for all nine beams is a challenging task, resulting in errors due to their pointing differences within the array. This paper introduces an iterative algorithm designed to obtain high-precision multi-beam pointing errors and to reconstruct the wavefront of the optical system under test. This enables a more accurate measurement of wavefront aberrations in the optical system to be tested. Firstly, simulation models were implemented to validate the algorithm's feasibility. Additionally, a scanning optical measurement system with a multi-beam array was developed in our lab, and the iterative algorithm was applied to process our experimental data. The results were then compared with interferometer data, demonstrating that our algorithm is feasible for MASTS to measure aberrations in large-aperture optical systems with high accuracy.