This paper aims to introduce an estimation algorithm for the joint densityof a circular-circular random variable, which is expressible in the form asdiscussed by Fernández-Durán (2007). The performance of the algorithm hasbeen checked with the help of a simulation study and it is found to performeciently even for small sample sizes. Furthermore, the performance of theproposed algorithm is compared with that of an existing method of densityestimation and is found to perform better than the existing one, which isindicated by the higher mean square error values for the estimates obtainedby the latter method. Finally, the application of the algorithm is displayedby estimating the joint density of a circular-circular random variable arisingin a real-life data set
