To overcome the extended Kalman Filter (EKF) limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformation. However, the ordinary UT has both local and global sampling problems. In this paper, non-symmetric unscented transformation (NSUT) is proposed to solve these problems. The sigma point sets of the NSUT are non-symmetrically located with respect to the zeroth sigma point set which is equal to the prior mean. Then, the weights of the sigma points are derived by using some conditions for mean and covariance. The non-symmetric unscented Kalman filter (NSUKF) based on the sigma points and weights of the NSUT are applied to the in-flight alignment (IFA) with a large heading error. With a low cost MEMS IMU, the simulations are can-jed out at an S-type trajectory to analyze the performance of the proposed method.