Abstract: By applying hypergraph theory, Algorithm RFCMHGT is presented for determing the realizability of a given directed fundamental cutset matrix Q_f and synthesizing its corresponding directed graph G layer by layer from its tree path submatrix Q_fp. Its principle is intuitive, and its computational complexity is O(nl²), where n and l are the numbers of rows and columns of Q_fp. Example 2 shows that Tutte's condition is not the sufficient condition for Q_f to he realizable.