In this paper, a new technique to realize lumped dual-band impedance transformers for arbitrary frequency-dependent complex loads is proposed. For the complex impedance transforming, closed-form design equations are presented for a series-shunt and a shunt-series type and a concept of combination is also presented. They use the proposed equation of input impedance. This equation can easily and exactly obtain the input impedance of any two-port network using the ABCD matrix. Then, in order to realize dual-band operation, four topologies comprising two types and a design method are presented. This technique is numerically demonstrated by various examples with excellent results and it has advantages of simplicity, intuitiveness and versatility because it is a general solution for complex impedance transforming. The proposed dual-band impedance transforming technique can be utilized for practical matching problems such as microwave amplifiers and other devices.