Multi-terminal high-voltage DC (HVDC) systems equipped with HVDC breakers require that detection and clearing of faults occur within a few milliseconds. Although detection without communication is generally preferred with regard to detection delay and simplicity, detection schemes relying on communication can enhance the overall performance due to their reliability. One such principle is the travelling wave differential protection that is based on the comparison of waves at both ends rather than solely on current. However, as with conventional differential protections, some kind of synchronisation must be applied to properly compensate for the time difference between samples obtained at different geographical locations. In this study, a synchronisation algorithm is presented that applies real-time signal processing to automatically obtain a proper compensation between the signals from both ends. The algorithm is examined by injection of data samples, generated from the simulation of an external fault in a PSCAD/EMTDC model. Additionally, the suitability for a real-time implementation is evaluated by execution time estimation using a simulated DSP. The algorithm is found to perform well, not only in identifying the compensation delay but also in terms of computational efficiency, thus allowing for real-time application.