  We consider the semiclassical dynamics of CGHS black holes with a
Weyl-invariant effective action for conformal matter. The trace anomaly of
Polyakov effective action is converted into the Virasoro anomaly thus leading
to the same flux of Hawking radiation. The covariance of semiclassical
equations can be restored through a non-local redefinition of the
metric-dilaton fields. The resulting theory turns out to be equivalent to the
RST model. This provides a mechanism to solve semiclassical equations of 2D
dilaton gravity coupled to conformal matter for classically soluble models.
