  An exact non-perturbative calculation of the fourth-order anomalous
correction to the scaling behaviour of a random shell-model for passive scalars
is presented. Importance of ultraviolet (UV) and infrared (IR) boundary
conditions on the inertial scaling properties are determined. We find that
anomalous behaviour is given by the null-space of the inertial operator and we
prove strong UV and IR independence of the anomalous exponent. A limiting case
where diffusive behaviour can influence inertial properties is also presented.
