The Einstein-Hilbert Lagrangian density in a two-dimensional spacetime is an exact differential

Recently Kiriushcheva and Kuzmin(1) claimed to have shown that the Einstein-Hilbert Lagrangian density cannot be written in any coordinate gauge as an exact differential in a two-dimensional spacetime. Since this is contrary to other statements on the subject found in the literature, as e.g., by Deser,(2) Deser and Jackiw,(3) Jackiw(4) and Grumiller, Kummer and Vassilevich(5) it is necessary to decide who has reason. This is done in this paper in a very simply way using the Clifford bundle formalism.