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The thermal instability of a rotating Rivlin-Ericksen viscoelastic fluid in the presence of uniform vertical magnetic field is considered. For the case of stationary convection, Rivlin-Ericksen viscoelastic fluid behaves like a Newtonian fluid. It is found that rotation has a stabilizing effect, whereas the magnetic field has both stabilizing and destabilizing effects. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The rotation and magnetic field are found to introduce oscillatory modes in the system which were nonexistent in their absence.