Abstract: Based on singular perturbation,strapdown inertial navigation system(SINS) with small parameters is analyzed.The strapdown algorithm is rearranged after predigesting the states equations in two-time scales.The inner boundary layer accounts for the thrust velocity.A new sculling compensation algorithm is designed to deal with the updating attitude during the specific force transformation.The outer boundary layer gives the gravitational velocity computation and velocity update on navigation frame.The simulation results showed that the accuracy of the new algorithm is similar as the four-sample Savage algorithm.Yet it requires less computational quantity.