  The relative center-of-mass energy spread at $e^+e^-$ colliders is about
$10^{-3}$, which is much larger than the widths of narrow resonances produced
in the s-channel in $e^+e^-$ collisions. This circumstance greatly lowers the
resonance production rates of J/Psi, Upsilon(1S), Upsilon(2S), Upsilon(3S) and
makes it extremely difficult to observe resonance production of the Higgs
boson. Thus, a significant reduction of the center-of-mass energy spread would
open up great opportunities in the search for new physics in rare decays of
narrow resonances, the search for new narrow states with small
$\Gamma_{e^+e^-}$, the study of true muonium and tauonium, etc. The existing
monochromatization scheme is only suitable for head-on collisions, while
$e^+e^-$ colliders with crossing angles (the so-called Crab Waist collision
scheme) can provide significantly higher luminosity due to reduced collision
effects. In this paper, we propose a new monochromatization method for
colliders with a large crossing angle. The contribution of the beam energy
spread to the spread of the center-of-mass energy is canceled by introducing an
appropriate energy-angle correlation at the interaction point; $\sigma_W/W \sim
(3-5)10^{-6}$ appears possible. Limitations of the proposed method are also
considered.
