We present a method to reduce the noise in the interaction matrix by calibration of the adaptive optics system.The method utilizes a matching between the actuators on the deformable mirror and the sub-apertures on thewavefront sensor to dene a lter matrix. Then, the lter matrix is applied to the sparse interaction matrix toremove the elements that should be zero. This method is useful for high-order systems and/or noise calibrationissues. The latter case is illustrated in the problem of on-sky calibration of an adaptive secondary system on atelescope, with a natural guide star, in which the noise in the interaction matrix is increased by the eects ofthe turbulent atmosphere.