Abstract <p>A new algorithm for finding the global minimizer of a one-dimensional multimodal function satisfying the Lipschitz condition with an unknown constant is considered and justified. It is assumed that the value of the function at the global minimizer is known (as is typical, e.g., in problems of minimizing the discrepancy between computed and experimental data). The convergence of the new algorithm is proved without using estimates of the Lipschitz constant, which are required in other Lipschitz optimization methods. Results of a numerical comparison of the efficiency of the proposed method with three well-known Lipschitz minimization algorithms are presented for functions from large random samples generated by two test-problem generators widely used in such studies.</p>