In this study, we are focused on thinning branching noisy data sets into curves. Robust Line Fitting (RLF) method is proposed for local linear region determination and also overcome problems which occur in high curvature regions. The performance of the RLF method is tested on different noisy branching data sets. These sets are generated artificially in three separation angles (30 degrees, 60 degrees, 90 degrees) and different noise levels (0.1, 0.2, 0.3). To the best of our knowledge, there is no study about non-simple noisy curve reconstruction. Thus, a comparison is made with our previous method which is useful only for simple noisy point clouds. As a result, RLF is an efficient method for not only simple curves but also non-simple curves.