  We discuss lowering the order of the two-dimensional scalar-tensor $R^2$
quantum gravity, by mapping the most general version of the model to a
multi-dilaton gravity, which is essentially the sigma-model coupled with
Jackiw-Teitelboim-like gravity. In the continuation of our previous research,
we calculate the divergent part of the one-loop effective action in a 2D
scalar-tensor (dilatonic) gravity with Ra2-term, which belongs to a specific
degenerate case and cannot be obtained from the general expression. The
corresponding finiteness conditions are found.
