  The study of the perturbative Odderon at high gluon densities in the color
glass condensate requires to take into account states with more than three
gluons. We formulate evolution equations for these states in which the number
of gluons is not fixed during the evolution. We further determine the coupling
of these Odderon states to the gamma to eta_c impact factor for arbitrary
numbers of gluons. We find an exact solution of the evolution equation for the
four-gluon Odderon state in terms of the three-gluon Odderon state. It is shown
that a similar solution exists also for a different class of Odderon solutions
which does not couple to the gamma to eta_c impact factor. We discuss the
implications of our result from the perspective of constructing an effective
field theory of reggeized gluons for the color glass condensate.
