For the operation of the practical software systems, the development, extension and modification phases are successively needed through the new requirements added and their errors debugging detected. Therefore, if it is possible to integrated the reusable software components and to reorganize them into the new software systems, we can improve the productivity, quality, and cost-effectiveness for he development of software systems. For these reasons, it will be required to research and develop methodology and tools for programs integration which make some programs merged effectively. In the process of merging two versions of a program into one, we can consider that some parts of the two versions are equivalent under the non-interference between them. According to the previous studies the program selected to determine the criterion of non-interference between them. According to the previous studies the program selected to determine the criterion of non-interference was very large, so we have difficulty in integrating many programs practically. In this paper, we propose a new improved algorithm which can reduce the related program size of non-interference criterion yb use of dynamic slicing techniques for integration of two versions of a program, and prove the efficiency of the proposed algorithm by showing some examples.