Detection of relationship between two time series is so important in different scientific fields. Most common techniques are usually sensitive to stationarity or normality assumptions. In this research, a new copula-based method (cyclocopula) is introduced to detect the relationship between two cylostationary time series with fractional Brownian motion (fBm) errors. The performance of the proposed method is studied by employing numerous simulated datasets. The applicability of the introduced approach is also investigated in real-world problems. The numerical and applied studies verify the performance of the introduced technique.