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This communication presents a new multistep matched-field algorithm for geoacoustic inversion by subspace extraction with a threshold. In this algorithm, according to the varying sensitivities of geoacoustic parameters, parameters are separated into several subsets (or subspaces). Then, inversions are carried out in each sensitive subspace using an optimization algorithm, and for each inversion, a sub-subspace is extracted where values of objective functions are lower than a given threshold. Finally, in all the extracted sub-subspaces combined with the subspace of insensitive parameters, an inversion is performed for all parameters to find the optimal solution. After the extracting process, the search space is greatly reduced, and generally, the true parameter values will not be excluded from the sub-subspace if a reasonable threshold is designed. Thus, higher efficiency and accuracy can be obtained when compared with other algorithms. Simulation is carried out on synthetic data and results indicate that the new algorithm's performance is significantly superior to those of other algorithms.