We have used molecular hydrogen transitions in high quality spectra of quasars Q0403-443, Q0347-383 and Q0528-250, to search for a change in the proton-to-electron mass ratio, mu. Our improvement on previous works is twofold. Firstly, we use an improved technique to calibrate the wavelength scale of the VLT/UVES data, which reduces systematics. Secondly, we model all the hydrogen Lyman alpha transitions in the vicinity of each molecular hydrogen transition. The motivation for doing so is to reduce systematic effects associated with the use of low order polynomial continuum approximations near the molecular hydrogen transitions. We find a fractional change, delta(mu)/mu of (+2.6 ± 3.0) x 10^(-6). Our measurement error is a factor of two improvement over Reinhold et al [PRL 96, 151101 (2006)] who find a 4-sigma detection of (+24 +/- 6) x 10^(-6). The new result we present in this paper, coupled with the previous results on varying alpha, appear inconsistent with generic predictions from Grand Unified Theories, suggesting either the latter are invalid, or the varying alpha results wrong.