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Attitude determination of the space vehicle always plays a pivotal role in space missions. Usually, the fourth-order Runge Kutta algorithm is taken as more common attitude integration algorithm. However, more appropriate algorithms are desired in order to meet variable requirement. This paper investigates the performance of the fourth-order Runge Kutta and Taylor series algorithms in coning environment, and presents a new algorithm which takes advantages from above both. Series of simulation experiments have been conducted to verify the effect of the new algorithm. Their results show that the new algorithm outperforms the fourth-order Runge Kutta and the four-sample rotation vector algorithms over long-duration run even in complex engineering applications where the attitude change is not too fast. [ABSTRACT FROM AUTHOR]