[en] Numerical modelling of the lateral-torsional buckling of steel beams at elevated temperature has shown that the beam design curve from EN 1993-1-2 is over-conservative in the case of non-uniform bending. Based on the newly proposed methodology for cold design from the EN 1993-1-1, an improved proposal for the lateral-torsional buckling of unrestrained steel beams subjected to fire is presented in this paper that addresses the issue of the influence of the loading type, the steel grade, the pattern of the residual stresses (hot-rolled or welded sections) and the ratio h/b, between the depth h and the width b of the cross-section on the resistance of the beam, achieving better agreement with the numerical behaviour while maintaining safety. The proposal is found to be safe and accurate through an extensive comparison with the results of FEM numerical simulations of more than 5000 beams. A statistical study of the results is performed, showing the accuracy of the improved proposal presented in this paper. (C) 2007 Elsevier Ltd. All rights reserved.