  The anomalous scaling behavior of the n-th order correlation functions ${\cal
F}_n$ of the Kraichnan model of turbulent passive scalar advection is believed
to be dominated by the homogeneous solutions (zero-modes) of the Kraichnan
equation $\hat{\cal B}_n {\cal F}_n=0$. Previous analysis found zero-modes in
perturbation theory in a small parameter. We present non-perturbative analysis
of the simplest (non-trivial) case of n=3 and compare the results with the
perturbative predictions.
