The transverse navigation system has been designed and developed to solve the challenges of navigation in polar regions. However, considerable theoretical errors are introduced into the system when the spherical Earth model is adopted. To tackle this problem, a transverse navigation mechanism under the ellipsoidal Earth model has been proposed in this research and the application regions of the proposed algorithm are specified and evaluated through error analysis. The analysis shows the presented transverse navigation system works in both polar and part of the non-polar regions. Field tests were conducted to evaluate the navigation performance in Nanjing, a non-polar region. A novel experimental method, where the field test data in mid-latitude areas was used to simulate the real Inertial Measurement Unit (IMU) data and the reference information in polar regions, was adopted to investigate the performance of the proposed algorithm in polar areas. The results show: that in the mid-latitude areas, the presented transverse navigation system achieves the same accuracy as the traditional inertial navigation system and that in polar regions, the proposed transverse mechanism outperforms the traditional method with a much lower error in longitude and yaw.