The paper describes a novel carrierphase synchronisation process that has been developed for use in a digital communication system operating over a satellite link and employing unbalanced quaternary phase shift keyed (UQPSK) signals. The satellite is not geostationary and may travel close to the surface of the earth over at least a part of its orbit. Correct carrier phase synchronisation needs to be achieved here as soon as the satellite rises above the horizon, during the time it is transmitting data signals, and therefore without the use of a known training signal. Under these conditions the digital signal is received at a low signal to noise ratio and in the presence of a severe Doppler shift. Correct carrier phase synchronisation must then be maintained as the satellite passes overhead and until it approaches the horizon again. Thus the synchronisation circuits must tolerate also a high rate of change of Doppler shift, albeit at a higher signal to noise ratio.The synchronisation algorithm is in two separate parts that operate sequentially and are both non-data aided. The first part removes the Doppler shift from the received signal and the second part then achieves carrier phase synchronisation, which is maintained over the rest of the transmission.The paper describes the new algorithms and presents the results of a series of computer simulation tests to assess their performances.