One of the central problems in the theory of synthesis of antennas is the question of the approximation of the specified direction diagram (RP) by entire functions of an exponential type; i.e., we are given functions of class   [1]. In fact, if the specified RP belongs to these functions, the problem of synthesis has an exact solution. It is known [2] that in practice the required RP of an antenna usually does not belong to these functions; therefore, they can acquire various forms. In this case, the problem of synthesis has no exact solution and the question of its approximate solving may be posed. Moreover, it will be possible to define the distribution of a current (field) on an aperture ensuring a specific RP with a required accuracy.