The configuration-fixed constrained triaxial relativistic mean-field approach is extended by including time-odd fields and applied to the study of the candidate multiple chiral doublets (MχD) nucleus Rh106. The energy contribution from time-odd fields and microscopical evaluation of center-of-mass correction as well as the modification of triaxial deformation parameters β,γ due to the time-odd fields are investigated. The contributions of the time-odd fields to the total energy are 0.1-0.3 MeV, and they modify slightly the β,γ values. However, the previously predicted multiple chiral doublets still exist. © 2009 The American Physical Society.