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Abstract In recent years, recommendation explanation methods have received widespread attention due to their potentials to enhance user experience and streamline transactions. In scenarios where auxiliary information such as text and attributes are lacking, counterfactual explanation has emerged as a crucial technique for explaining recommendations. However, existing counterfactual explanation methods encounter two primary challenges. First, a substantial bias indeed exists in the calculation of the group impact function, leading to the inaccurate predictions as the counterfactual explanation group expands. In addition, the importance of collaborative filtering as a counterfactual explanation is overlooked, which results in lengthy, narrow, and inaccurate explanations. To address such issues, we propose a counterfactual explanation method based on Modified Group Influence Function for recommendation. In particular, via a rigorous formula derivation, we demonstrate that a simple summation of individual influence functions cannot reflect the group impact in recommendations. After that, building upon the improved influence function, we construct the counterfactual groups by iteratively incorporating the individuals from the training samples, which possess the greatest influence on the recommended results, and continuously adjusting the parameters to ensure accuracy. Finally, we expand the scope of searching for counterfactual groups by incorporating the collaborative filtering information from different users. To evaluate the effectiveness of our method, we employ it to explain the recommendations generated by two common recommendation models, i.e., Matrix Factorization and Neural Collaborative Filtering, on two publicly available datasets. The evaluation of the proposed counterfactual explanation method showcases its superior performance in providing counterfactual explanations. In the most significant case, our proposed method achieves a 17% lead in terms of Counterfactual precision compared to the best baseline explanation method.