<p>For solving the linear systems with multiple right-hand sides, we propose the global double greedy block Kaczmarz method. The traditional single greedy criterion considers the larger entries of the residual matrix to select the working row or construct the working block, which may lead to an increase in smaller entries of the residual matrix during the iterative process, known as the “seesaw effect”. In this paper, we introduce a double greedy strategy aimed at reducing this effect. Theoretical analysis shows that this strategy is superior to the single greedy criterion. Numerical results further demonstrate the effectiveness of our proposed method.</p>