  In this paper, we give a procedure for discretizing recursion operators by
utilizing unified bilinear forms within integrable hierarchies. To illustrate
this approach, we present unified bilinear forms for both the AKNS hierarchy
and the KdV hierarchy, derived from their respective recursion operators.
Leveraging the inherent connection between soliton equations and their
auto-B\"acklund transformations, we discretize the bilinear integrable
hierarchies and derive discrete recursion operators. These discrete recursion
operators exhibit convergence towards the original continuous forms when
subjected to a standard limiting process.
