It is well known as the coning effect that even the motion around an axis with no angular rate results in the residual rotation when it resumes the original orientation. However, there has been little investigation concerning the residual rotation when the motion is not closed and does not resume the original orientation. A definition of rotation angle is newly proposed in this paper, and the calculation method of the rotation angle is shown. The new attitude reference system with a one-degree-of-freedom platform was developed using the rotation angle defined in this paper and two parameters showing the rotational axis orientation. The attitude reference system was actually onboard the M-rocket, and it worked well.