Summary. We propose a discrete time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. A further discussion is given on some submodels, in particular on the stationary process. The proposed model is compared with some existing Markov processes for circular data. Some statistical issues of the model, such as statistical inference, model selection and diagnostic checks, are considered. Finally, an application of the model to wind direction data is provided.