The decorrelation in the azimuthal angle between the most forward and the most backward jets (Mueller-Navelet jets) is measured in data collected in pp collisions with the CMS detector at the LHC at root s = 7 TeV. The measurement is presented in the form of distributions of azimuthal-angle differences, Delta phi, between the Mueller-Navelet jets, the average cosines of (pi - Delta phi), 2(pi - Delta phi), and 3(pi - Delta phi), and ratios of these cosines. The jets are required to have transverse momenta, p(T), in excess of 35 GeV and rapidities, |y|, of less than 4.7. The results are presented as a function of the rapidity separation, Delta y, between the Mueller-Navelet jets, reaching Delta y up to 9.4 for the first time. The results are compared to predictions of various Monte Carlo event generators and to analytical predictions based on the DGLAP and BFKL parton evolution schemes.