Abstract: As the Euler-d'Alembert theorem demonstrated, the finite displacement of a rigid body that rotates around a fixed point can be realized by rotating around the eigenaxis. This paper introduces a simple method for determining the eigenaxis and the corresponding rotational angle when a rigid body rotates from one attitude to another, it also provides the formula of calculating the direction of the eigenaxis by Euler angles. Compared with the way of solving the eigenvector of the coordinate matrix, the method proposed in this paper has lower computational complexity and is more convenient to use.