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To achieve more efficient blind separation of multi-channel speech signals, this paper proposes a new algorithm for blind source separation(BSS) of sound sources using auxiliary function-based independent vector analysis (AuxIVA) with joint pairwise updates of demixing vectors. This algorithm is better than AuxIVA using iterative projection with adjustment (AuxIVA-IPA) when separating multiple sources. The IPA method jointly executes iterative projection (IP) and iterative source steering (ISS) to update and updates one row and one column of the separation matrix in each iteration. On this basis, IPA is extended to jointly execute IP2 and ISS2 for updating, which can update two rows and two columns of the separation matrix in each iteration. Accordingly, this proposed method is named by IPA2. Furthermore, it can optimize the same cost function as IPA while maintaining the same time complexity. Finally, the convolutional speech separation experiments are conducted to validate the effectiveness and efficiency of the proposed method. The experimental results corroborate that compared with the state-of-the-art IP, IP2, ISS, ISS2, and IPA used in AuxIVA, the IPA2 method acquires faster convergence speed and better separation performance, enabling the cost function to reach the convergence interval faster and maintaining good separation results.