  We consider exactly solvable semi-classical theory of two dimensional
dilatonic gravity with electromagnetic interactions. As was done in the paper
by Russo, Susskind and Thorlacius, the term which changes the kinetic term is
added to the action. The theory contains massless fermions as matter fields and
there appear the quantum corrections including chiral anomaly. The screening
effect due to the chiral anomaly has a tendency to cloak the singularity. In a
region of the parameter space, the essential behavior of the theory is similar
to that of Callan, Giddings, Harvey and Strominger's dilatonic black hole
theory modified in the paper by Russo, Susskind and Thorlacius and the
singularity formed by the collapsing matter emerges naked. We find, however,
another region of the parameter space where the singularity disappears in a
finite proper time. Furthermore, in the region of the parameter space, there
appears a discontinuity in the metric on the trajectory of the collapsing
matter, which would be a signal of topology change
