In evaluating the relative risk of seasonality, the null value is a boundary value. In this case, tests for the null hypothesis exist, but standard methods for confidence intervals are not appropriate. We provide a method for constructing confidence intervals under the circular normal model. The proposed confidence intervals are valid for all values of the underlying seasonal risk if the model is correct and for the null boundary value of the seasonal risk, regardless of model assumptions and sample size. We apply our method to seasonal suicide data from a recent report.