In this paper, we give a new algorithm evolving from Atallah's algorithm proposed in 1984, and we make many improvements: First, combining replaced sewing in order to simplify the third step, Second, we delete the fourth step. And we simplify the construction of the auxiliary graph, avoiding the second time to find Euler tour and the introduction of a mass storage array. The improvements make it quicker and simpler to find the Euler tour of an Euler graph, and the improvements don't increase time and space complexity of Atallah's algorithm.