For accurate a posteriori error analysis of the reduced basis method for coercive and non-coercive problems, a critical ingredient lies in the evaluation of a lower bound for the coercivity or inf-sup constant. In this short Note, we generalize and improve the successive constraint method first presented by Huynh (2007) by providing a monotonic version of this algorithm that leads to both more stable evaluations and fewer offline computations. To cite this article: Y Chen et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). (C) 2008 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.