Recently, there is strong interest on the subject of outlier problem in circular data. In this paper, we focus on detecting outliers in a circular regression model proposed by Down and Mardia. The basic properties of the model are available including the exact form of covariance matrix of the parameters. Hence, we intend to identify outliers in the model by looking at the effect of the outliers on the covariance matrix. The method resembles closely the COVRATIO statistic for the case of linear regression problem. The corresponding critical values and the performance of the outlier detection procedure are studied via simulations. For illustration, we apply the procedure on the wind data set.