A method of reduction of order for discrete systems

We show how, by establishing a suitable Backlund correspondence, a reduction in order can be effected for discrete systems having a certain structure. In this way we succeed in extending to discrete systems ideas previously developed within the context of ordinary differential equations. It is also worth emphasizing that our approach represents an application of properties characteristic of completely integrable systems outside of that context, that is, to systems of discrete equations, integrable or otherwise.