  We propose an algebraic scheme for quantizing the rational
Ruijsenaars-Schneider model in the R-matrix formalism. We introduce a special
parameterization of the cotangent bundle over GL(N,C). In new variables the
standard symplectic structure is described by a classical (Frobenius) r-matrix
and by a new dynamical $\bar{r}$-matrix. Quantizing both of them we find the
quantum L-operator algebra and construct its particular representation
corresponding to the rational Ruijsenaars-Schneider system. Using the dual
parameterization of the cotangent bundle we also derive the algebra for the
L-operator of the trigonometric Calogero-Moser system.
