The technique of control of stability of points of the planned geodetic network which essence consists in a consecutive exception of the points which shifts surpass limiting errors of their definition is offered. As basic data coordinates of points and an assessment of their accuracy serve in an initial cycle of supervision (an initial network) and in a studied cycle of supervision (a studied network). Basic data are determined by a studied network by a way of preliminary equalizing of a network as free. The presented technique is considered on an example of a geodetic network of construction of the 2nd scene of the Maryinsky Theater in St. Petersburg.