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This study concerns the fast and accurate solution of multilevel non-LTE radiation transfer problems. We propose and evaluate an alternative iterative scheme to the classical MALI method. Our study is instead based on the application of Broyden’s method for the solution of nonlinear systems of equations. Comparative tests, in 1D plane-parallel geometry, of the popular MALI method and our alternative method are discussed. The Broyden method is typically 4.5 times faster than MALI. This makes it also fairly competitive with the Gauss-Seidel and Successive Over-Relaxation methods developed after MALI.