The relative center-of-mass energy spread σW∕W at e+e− colliders is 𝒪(10−3), which is much larger than the widths of narrow resonances J∕ψ, ψ(2S), ϒ(1S), ϒ(2S), ϒ(3S) mesons, tauonium and some others. Its reduction would significantly increase the resonance production rates and open up great opportunities in the search for new physics. In this paper, we propose a new monochromatization method for colliders with a large crossing angle (which can provide a high luminosity). The contribution of the beam energy spread to σW is canceled by introducing an appropriate energy–angle correlation at the interaction point; σW∕W∼(0.5−1)×10−5 appears possible.