In this work, we present a Deuteron Nuclear Magnetic Resonance (DNMR) study of the non-symmetric odd liquid crystal dimer a-(4-cyanobiphenyl-4'-yloxy)-¿-(1-pyrenimine-benzylidene-4'-oxy) heptane (CBO7O.Py), formed by a pro-mesogenic cyanobiphenyl unit and a bulky pyrene-containing unit, linked via alkoxy flexible chain. We have synthesized two partially deuterated samples: one with the deuterium atoms in the cyanobiphenyl moiety (dCBO7O.Py) and the other one with the deuterium atoms in the pyrenimine-benzylidene unit (CBO7O.dPy). We have performed angular distribution analysis in the SmA glassy state, obtaining the degree of order of both rigid cores and an estimation of the internal molecular angle between both structures. With the results from the angular study, we have been able to determine the degree of order of both rigid units in either the N phase and the SmA phase, far enough from the glass transition. Both rigid cores have the same degree of order close to the nematic–isotropic phase transition, but as the compound is cooled down, the degree of order of the cyanobiphenyl moiety is clearly higher than that of the pyrene-containing unit. The critical behaviour of the order parameter of the pyrene-containing moiety is consistent with the fact that, for CBO7O.Py, the N–I phase transition is tricritical, which seems to indicate that the uniaxial order parameter of the dimer is dominated by the degree of order of the pyrene-containing core.