We study in this work the decay of the electric birefringence from the steady-state value to zero when an orienting electric field applied on a macromolecule is switched off. We consider specifically the case of segmentally flexible macromolecule with only two subunits and one hinge. Using Brownian dynamics as the predicting tool for the dynamics of the molecule, we have paid special attention to important aspects such as hydrodynamic interaction, field strength, and orienting mechanism, improving statistics to obtain data with very good signal-to-noise ratio, we have found a different behavior of the induced and permanent dipoles in the relaxation process: the first one can be described independently of the intensity of the field while the second shows a dependence of the field strength. Moreover, the time spectrum shows no dependence on the type of dipole or the field intensity, and amplitudes appear to be essential in characterizing the relaxation of the molecule. According to our results, hydrodynamic interaction could be very important in describing the relaxation times of a molecule, but amplitudes are not affected by this refinement, which should be a very interesting advantage for the application and development of different simplified theories.