The attitude arithmetic is one of the important parts in strapdown inertial navigation system (SINS). Based on traditional three order recursive Taylor expansion and four-order Range-Kuttle method, another effective method four-order Taylor expansion was proposed. Under the typical circular cone rotation condition, the three algorithms were simulated on angle error. Considered precision and speed, the simulation result proves that the four-order recursive Taylor expansion is better than the three-order recursive Taylor expansion and the four-order Range Kuttle method. And this method offers reference for developing attitude arithmetic of SINS.