Cluster analysis is widely used in data analysis. Statistical data analysis is generally performed on the linear data. If the data has directional structure, classical statistical methods cannot be applied directly to it. This study aims to improve a new directional clustering algorithm which is based on trigonometric approximation. The trigonometric approximation is used for both descriptive statistics and clustering of directional data. In this paper, the fuzzy clustering algorithms (FCD and FCM4DD) improved for directional data and the proposed method are carried out on some numerical and real data examples, and the simulation results are presented. Consequently, these results indicate that the fuzzy c-means directional clustering algorithm gives the better results from the points of the mean square error and the standard deviation for cluster centers.