The article presents a method of correcting the positioning accuracy of the Tip/Tilt Mirror (TTM) system with a milliradian range of angular movements. The correction is aimed at eliminating the influence of the kinematics of the system exchanging linear movement of activators (controlled in a closed loop control) into angular movement of the mirror in XY axes. Using a specially designed test rig, comprising of a laser and a detector with a CCD matrix (described in the article), the actual angular positions of the mirror are measured. The data acquisition system is based on NI technology and LabView software. The measurement is performed automatically. The obtained results show the difference between the actual and set positions, and after tabulating allow - during a normal operation of the mirror - to introduce corrections to the control signal in the real time. Due to a systematic nature of the positioning error,  a polynomial correction function was adjusted, which eliminates the necessity to draw values from the matrix, replacing this operation with an appropriate multiplication of a control signal. As a result of applying this method, a high linearity and repeatability of mirror positioning was achieved.