The authors consider an analogue of the Painlevé property for discrete equations. They start from a difference equations of the type
with being rational in both arguments, , , , . The discrete version of the Painlevé II equation for which
with constant parameters belongs to this class of equations. For this equation the “integrability” test based on singularity confinement for meromorphic solutions is applied; this confinement is discussed using the Nevanlinna theory.