Flexible HVDC technology is powerful in addressing the integration of large-scale renewable energy, and its line protection is key to ensuring system safety and stability. Single-ended protection of the line does not require communication and can better meet the time requirements of flexible HVDC transmission systems. However, the performance of existing single-ended protection in flexible HVDC transmission systems is significantly affected by subsequent traveling waves, resulting in a certain range of protection dead zones. To address this, based on fully considering the impact of subsequent traveling waves on the initial traveling wave, the differences between internal and external fault traveling waves are explored, and a fault identification criterion based on waveform matching is proposed. This criterion can measure the impact of subsequent traveling waves by combining matching errors with matching waveform characteristics, ultimately achieving full-line rapid protection. A four-terminal flexible DC transmission system is built based on PSCAD/EMTDC. Simulation results verify the feasibility of the proposed method, which has the advantages of a long protection range, strong tolerance to transition resistance, and strong anti-noise interference capability.