This brief proposes an innovational method to design a broadband high-efficiency transistor-based rectifier with high rectification efficiency. The theory of the class-F⁻¹ rectifier with the input second harmonic component is explored. Moreover, the mathematical variations of rectification efficiency and load/source impedances versus several crucial design parameters are established. The variation relationships indicate that the rectification efficiency can roughly maintain constant across a large input second harmonic range, resulting in more available design impedances. Thus, this provides the possibility to design wideband rectifiers. For validation, a broadband high-efficiency class-F⁻¹ rectifier (operating in 1.6–2.6 GHz) using a GaN transistor is designed, assembled, and measured. Measurements indicate a rectification efficiency of between 72.1% and 82.4% under the condition of R_dc = 67 Ω and P_in = 40 dBm. The realized rectifier exhibits the largest relative bandwidth compared with transistor-based rectifiers reported before. The methodology presented in this brief provides a promising approach for broadband high-efficiency GaN HEMT-based rectifiers.