The decays of pseudoscalar bottomonium ηb into a pair of vector charmonia, J/ψJ/ψ, J/ψψ′, ψ′ψ′, are considered in the light cone formalism. Relativistic and leading logarithmic radiative corrections to the amplitudes of these processes are resummed. It is shown that the small value for the branching ratio of the decay ηb→J/ψJ/ψ obtained within the leading-order nonrelativistic QCD is a consequence of a fine-tuning between certain parameters, which is broken when relativistic and leading logarithmic radiative corrections are taken into account. As a result, the branching ratio obtained in this paper is enhanced by an order of magnitude.