We propose what we believe is a new model to quantitatively describe the lambda-phage SWITCH system. The model incorporates facilitated transfer mechanism of transcription factor, which can be simplified into a two-step reaction. We first sequentially obtain two indispensable parameters by fitting our model to experimental data of two simple systems, and then apply them to study the natural lambda-SWITCH system. By incorporating the facilitated transfer mechanism, we find that in RecA(-) host Escherichia coli, the wild-type lambda-lysogenic state is in a monostable regime rather than in a bistable regime. Furthermore, the model explains the weak role of Cro protein and probably sheds light on the evolution of lambda-Cro protein, which is known to be structurally distinct from the other Cros in lambdoid family members.