The authors have studied the linear stability of Couette flow between concentric rotating cylinders. The linearized Navier-Stokes equation of 6th order has two zeros and four purely imaginary eigenvalues at a suitable value of the speed of rotation of the outer cylinder. There is thus a reduced bifurcation equation on a six-dimensional space which can be shown to commute with an action of the symmetry group O(2)\(\times SO(2)\). Group structure is used to analyze this bifurcation equation in the simplest case and the stabilities of solutions are computed. In the case of counterrotating cylinders, transition is observed which confirms the experimental results. This method can be extended to many other situations in this field.