The problem of decoherence of two-state quantum systems interacting with a bath through an external controllable driving field without rotating wave approximation is discussed. The off-diagonal elements of density operator in two-state quantum systems are obtained. The result reflects that decoherence of the two-state quantum systems has something to do with its original state, frequency of the bath and external controllable driving field. The relation between the decoherence and external controllable driving field is studied. Properties of an external controllable driving field are obtained when the two-state quantum systems of coherence is maintained.