Abstract M-estimator using iteratively reweighted least squares (IRLS) is one of the best-known methods for robust estimation. However, IRLS is ineffective for robust unit-norm constrained linear fitting (UCLF) problems, such as fundamental matrix estimation because of a poor initial solution. We overcome this problem by developing a novel objective function and its optimization, named iteratively reweighted eigenvalues minimization (IREM). IREM is guaranteed to decrease the objective function and achieves fast convergence and high robustness. In robust fundamental matrix estimation, IREM performs approximately 5-500 times faster than random sampling consensus (RANSAC) while preserving comparable or superior robustness