We consider a version of QCD dipole cascading corresponding to a finite number n of discrete \Delta Y steps of branching in rapidity. Using the discretization scheme preserving the holomorphic factorizability and scale-invariance in position space of the dipole splitting function, we derive an exact recurrence formula from step to step which plays the rôle of a ``discrete-time'' Balitsky--Kovchegov equation. The BK solutions are recovered in the limit n=\infty and \Delta Y=0.

PACS numbers: 12.38.--t, 12.38.Cy