In this paper we propose a new state estimation algorithm called the extended information filter on Lie groups. The proposed filter is inspired by the extended Kalman filter on Lie groups and exhibits the advantages of the information filter with regard to multisensor update and decentralization, while keeping the accuracy of stochastic inference on Lie groups. We present the theoretical development and demonstrate its performance on multisensor rigid body attitude tracking by forming the state space on the SO(3)×R^3 group, where the first and second component represent the orientation and angular rates, respectively. The performance of the filter is compared with respect to the accuracy of attitude tracking with parametrization based on Euler angles and with respect to execution time of the extended Kalman filter formulation on Lie groups. The results show that the filter achieves higher performance consistency and smaller error by tracking the state directly on the Lie group and that it keeps smaller computational complexity of the information form with respect to high number of measurements.