This paper introduces a new method called Bidirectional Delta file, which is to construct a two way delta file out of two given files. Previous work focuses on forwards and backwards delta files. Here we suggest efficiently combining them into a single file. Given two files S and T, the paper designs a greedy algorithm, which produces an efficient bidirectional delta file in terms of the memory storage it requires. Given this encoding file and the original file S, one can decode it in order to produce T, and vice versa. Experiments show memory storage savings of at least 25% between the implemented algorithm and the traditional way of using both forwards and backwards delta files.