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The Fuzzy Linear Programming problem has been used as an important planning tool for the different disciplines such as engineering, business, finance, economics, etc. In this paper, we proposed a modified algorithm to find the fuzzy optimal solution of fully fuzzy linear programming problems with equality constraints. Recently, Ezzati et al. (Applied Mathematical Modelling, 39 (2015) 3183-3193) suggested a new algorithm to solve fully fuzzy linear programming problems. In this paper, we modified this algorithm and compare it with other existing methods. Furthermore, for illustration, some numerical examples and one real problem are used to demonstrate the correctness and usefulness of the proposed method.