By means of molecular dynamics simulations, dynamical properties of racemic ibuprofen glass-forming liquid are investigated at different temperatures from 360 to 500 K. The origin of the peculiar low amplitude Debye-type relaxation observed experimentally by dielectric relaxation spectroscopy is addressed (Bras, A. R.; Noronha, J. P.; Antunes, A. M. M.; Cardoso, M. M.; Schonhals, A.; Affouard, F.; Dionisio, M.; Correia, N. T. J. Phys. Chem. B 2008, 112, 11087). Single and total dipolar autocorrelation functions are calculated. It is found that the behavior of the total dipole correlation is dominated at short and long times by the single function. It mainly originates from the antiparallel dipoles correlations in agreement with a value of the Kirkwood correlation factor slightly smaller than unity. The simulation suggests that the long time Debye-type decay of the dipole-dipole correlation is dominated by the internal cis-trans conversion of the O=C-O-H group coupled to the change of the intermolecular linear/cyclic HB structures. The overall rotation of the molecules is about 1-2 decades faster than the cis to trans transformation, so all the O=C-O-H group environments are equal on average. The effective rotational potential energy barriers of the O=C-O-H H groups due to the surroundings are thus averaged and dipolar relaxation follows a simple Debye law. It is found that cyclic dimers inhibit the cis to trans conversion unlike the linear dimers and trimers which favor this conversion and stabilize the trans isomer. It is well in line with the very low amplitude of the dielectric strength associated with the Debye relaxation observed experimentally and its increase when the liquid is maintained isothermally above the melting temperature since this amplitude mainly relates to the low fraction of ibuprofen molecules in the trans conformation. A comparison is made with the Debye-type relaxation found in microstructured monohydroxy alcohols.