Similarity joins are recognized to be among the most useful data process- ing and analysis operations. A similarity join is used to retrieve all data pairs whose distances are smaller than a predefined threshold λ . In this paper, we introduce the MRS-join algorithm to perform similarity joins on large trajectories datasets. The MapReduce model and a randomized LSH (Local Sensitive Hashing) keys redistribution approach are used to balance load among pro- cessing nodes while reducing communications and computations to almost all rele- vant data by using distributed histograms. A cost analysis of the MRS-join algorithm shows that our approach is insensitive to data skew and guarantees perfect balancing properties, in large scale systems, during all stages of similarity join computations. These performances have been confirmed by a series of experiments using the Fréchet distance on large datasets of trajectories from real world and synthetic data benchmarks.