In the present work, the nematic glassy state of the non-symmetric LC dimer -(4-cyanobiphenyl-4-yloxy)--(1-pyrenimine-benzylidene-4-oxy) undecane is studied by means of calorimetric and dielectric measurements. The most striking result of the work is the presence of two different glass transition temperatures: one due to the freezing of the flip-flop motions of the bulkier unit of the dimer and the other, at a lower temperature, related to the freezing of the flip-flop and precessional motions of the cyanobiphenyl unit. This result shows the fact that glass transition is the consequence of the freezing of one or more coupled dynamic disorders and not of the disordered phase itself. In order to avoid crystallization when the bulk sample is cooled down, the LC dimer has been confined via the dispersion of -alumina nanoparticles, in several concentrations.