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We report a new constraint on the variation of the fine-structure constantbased on the analysis of 15 Si IV doublets selected from a ESO-UVES sample. Wefind \Delta\alpha/\alpha = (+0.15+/-0.43) x 10^-5 over a redshift range of1.59< z < 2.92 which is consistent with no variation in \alpha. This resultrepresents a factor of three improvement on the constraint on\Delta\alpha/\alpha based on Si IV doublets compared to the published resultsin the literature. The alkali doublet method used here avoids the implicitassumptions used in the many-multiplet method that chemical and ionizationinhomogeneities are negligible and isotopic abundances are close to theterrestrial value.Comment: 12 Pages, 7 figures. Accepted for publication in A&A. In addition to  minor corrections an appendix is added in this revised versio

Probing the time-variation of the fine-structure constant: Results based on Si IV doublets from a UVES sample