Summary: A necessary and sufficient condition for a special mixed graph (whose undirected edge set is a spanning tree) to be an Eulerian graph is given. Based on this condition and Guan and Pulleyblank’s algorithm, another algorithm for the minimum Eulerian orientation is given; see M. Guan and W. Pulleyblank [SIAM J. Algebraic Discrete Methods 6, 657-664 (1985; Zbl 0576.05046)].