  The general rational solution of the Yang-Baxter equation with the symmetry
algebra sl(2) can be represented as the product of the simpler building blocks
denoted as R-operators. The R-operators are constructed explicitly and have
simple structure. Using the R-operators we construct the two-parametric
Baxter's Q-operator for the generic inhomogeneous periodic XXX spin chain. In
the case of homogeneous XXX spin chain it is possible to reduce the general
Q-operator to the much simpler one-parametric operator.
