In this paper, a new indoor positioning system based on incident angle measurement of infrared lights has been suggested. Though there have been various researches on indoor positioning methods using vision sensor or ultrasonic sensor, they have not only advantages, but also disadvantages. To minimize the disadvantages they have, this new method using incident angle of infrared light has been invented. In a new positioning system, there are three infrared emitters on fixed known positions. An incident angle sensor measures the angle differences between each two emitters. Measured angle differences determine a position. This method is available only inside the triangle which is composed of three emitters. Mathematical problems to determine the position with angle differences and position information of emitters has been solved. To solve the non-linear equations without prior position information, iterative linearization process has been used. Simulations and experiments have been implemented to show the performance of this new positioning system. The results of simulation were good. Since there existed problems of noise and signal conditioning, the experimented has been implemented in limited area. But the results were acceptable. This new positioning method can be applied to any indoor systems that need absolute position informations.