A ring gear (114) for an epicyclic or planetary reduction gear (110) of a turbomachine, in particular of an aircraft, said ring gear extending about an axis and comprising first and second coaxial annular elements (114a, 114b) and comprising, respectively, two inner annular toothing sets (150) of different orientation, said first and second annular elements further comprising, respectively, first and second radially outer annular flanges (114ab, 114bb) for attaching said first and second elements to each other, characterised in that one of said first and second flanges comprises, at its outer periphery, a cylindrical centring rim (164) configured to cooperate with the outer periphery of the other of said first and second flanges.