Abstract: In the fields of aerospace and robotics, there are two quaternion expression conventions, Hamilton and JPL, for the rotation expression of rigid body. This directly leads to confusion and imprecision in the derivation of quaternion-based formulas, and introduces errors in engineering practice. Analyzing the origin of the two expression conventions, comparing the internal similarities and differences, especially the homomorphy with the attitude matrix when dealing with continuous rotation, two methods were proposed to discriminate and convert the quaternion convention, and were verified in experiments. Based on the analysis of history, practical application scope, operational efficiency, and application similarity of two expression conventions, some suggestions were made, including understand clearly for the expression conventions used in quaternion application, and gradually abandon the JPL conventions of quaternion.