Join operation is one of the key ones in databases, allowing to cross data from several tables. Two tuples are crossed when they share the same value on some attribute(s). A fuzzy or similarity join combines all pairs of tuples for which the distance is lower than or equal to a prespecified threshold ε from one or several relations. Fuzzy join has been studied by many researchers because its practical application. However, join is the most costly and may even not be possible to compute on large databases. In this paper, we thus propose the optimization for MapReduce algorithms to process fuzzy joins of binary strings using Hamming Distance. In particular we propose to use an extension of Bloom Filters to eliminate the redundant data, reduce the unnecessary comparisons, and avoid the duplicate output. We compare and evaluate analytically the algorithms with a cost model.