In the paper we propose and solve analytically the nonlinear evolution equation in the leading twist approximation for the odderon contribution. We found three qualitative features of this solution, which differs the odderon contribution from the Pomeron one: (i) the behavior in the vicinity of the saturation scale cannot be derived from the linear evolution in a dramatic difference with the Pomeron case; (ii) a substantial decrease of the odderon contribution with the energy; and (iii) the lack of geometric scaling behavior. The two last features have been seen in numerical attempts to solve the odderon equation.