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The estimation of a fundamental matrix between two views is of great interest for a number of computer vision and robotics tasks. There exist well-known algorithms for this problem: such as normalised eight-point algorithm, fundamental numerical scheme (FNS), extended FNS (EFNS), and heteroscedastic errors-in-variable (HEIV). The Levenberg-Marquardt (LM) method can also be employed to estimate a fundamental matrix; however, for some unknown reason, it was unfairly treated in the literature so that it was reported to have inferior performance. In this study, the authors concentrate on the application of the LM method for fundamental matrix estimation. Particularly, a new Gauss-Newton approximation of the Hessian matrix is presented, when the Sampson error is minimised; and the rank-two constraint of a fundamental matrix is automatically enforced by revitalising a particular parameterisation. An evaluation of algorithms is presented, showing the advantage of these two techniques.