High frequency current transformers (HFCTs) are widely employed to detect partial discharge (PD) induced currents in high voltage equipment. This paper describes measurements of the wideband transfer functions of HFCTs so that their influence on the detected pulse shape in advanced PD measurement applications can be characterized. The time-domain method based on the pulse response is a useful way to represent HFCT transfer functions as it allows numerical determination of the forward and reverse transfer functions of the sensor. However, while the method is accurate at high frequencies it can have limited resolution at low frequencies. In this paper, a composite time-domain method is presented to allow accurate characterization of the HFCT transfer functions at both low and high frequencies. The composite method was tested on two different HFCTs and the results indicate that the method can characterize their transfer functions ranging from several kHz to tens of MHz. Results are found to be in good agreement with frequency-domain measurements up to 50 MHz. Measurement procedures for using the method are summarized to facilitate further applications.