The algebraic solution for linear, ideal simulated moving-bed (SMB) chromatography derived previously revealed important new properties of the SMB process. This solution was validated by comparing with experimental data and with the results of numerical solutions of the equilibrium-dispersive and the lumped kinetic model. This earlier solution, however was limited to the simple case in which the safety factor was assumed to be the same for the flow rates in all four sections. An extension of this solution to the case in which the safety factors differ and allow an independent selection of the four different flow rates (within limits) is derived. This solution accounts well for most practical situations. It permits the discussion of the influence of different flow rates on the performance of an SMB unit, an issue of critical importance for the optimization of the design and operation of these separators.