This paper presents a new human motion tracking system using two wearable inertial sensors that are placed near the wrist and elbow joints of the upper limb. Each inertial sensor consists of a tri-axial accelerometer, a tri-axial gyroscope and a tri-axial magnetometer. The turning rates of the gyroscope were utilised for localising the wrist and elbow joints on the assumption that the two upper limb segment lengths are known a priori. To determine the translation and rotation of the shoulder joint, an equality-constrained optimisation technique is adopted to find an optimal solution, incorporating measurements from the tri-axial accelerometer and gyroscope. Experimental results demonstrate that this new system, compared to an optical motion tracker, has RMS position errors that are normally less than 0.01 m, and RMS angle errors that are 2.5-4.8 degrees .