Abstract: A new method of 3 rd order minimal parameter solution for the orthogonal matrix differential equation is modified and used to solve the quaternion differential equation, and the numerical simulation is done in the Strap-down Inertial Navigation System(SINS). The result shows that when the new algorithm is used, the precision of the solved attitude angle is about 3 to 5 times higher than that by using the classical method, but the floating-point operations is only about half of the old one. So it is an important method to improve the precision of SINS.