There are some limitations in the null test measurement in the stitching interferometry. In order to meet the null test conditions, the moving distance between the sub-apertures often deviates from the theoretical preset distance, which leads to a position deviation of sub-apertures under measurements. To overcome this problem, an algorithm for data processing is proposed. We used iterative calculation of the deviations between the sub-apertures to adjust their positions, to ensure the local validity of the linear approximation algorithm and realize the exact stitching. A cylindrical lens as an object for experimental examination of the proposed method was taken. The obtained results demonstrate the validity, reliability and feasibility of our iterative stitching algorithm.