Based on highly accurate laboratory measurements of Lyman bands of H2 and an updated representation of the structure of the ground XΣg+1 and excited BΣu+1 and CΠu1 states, a new set of sensitivity coefficients Ki is derived for all lines in the H2 spectrum, representing the dependence of their transition wavelengths on a possible variation of the proton-electron mass ratio μ=mp/me. Included are local perturbation effects between B and C levels and adiabatic corrections. The new wavelengths and Ki factors are used to compare with a recent set of highly accurate H2 spectral lines observed in the Q 0347-383 and Q 0405-443 quasars, yielding a fractional change in the mass ratio of Δμ/μ=(2.4±0.6)×10-5 for a weighted fit and Δμ/μ=(2.0±0.6)×10-5 for an unweighted fit. This result indicates, at a 3.5σ confidence level, that μ could have decreased in the past 12 Gyr. © 2006 The American Physical Society.