This paper focuses on detecting outliers in the circular data which follow the wrapped normal distribution. We considered four discordance tests based on M, C, D and A statistics. The cut-off points of the four tests were obtained and the performance of the detection procedures was studied via simulations. In general, we showed that the discordance test based on the A statistic outperforms the other tests in all cases. For illustration, the city of Kuantan wind direction data set was considered.