This paper presents an algorithm for the terminal synthesis of the orbital orientation for a spacecraft. The algorithm is based on solving the following problems: the analytical determination of the program values for the angular velocity vector components in an orbital coordinate system and the stabilization of the program values for the turn rate vector components and the desired terminal angular position of a spacecraft. The program values of the angular velocity vector components are determined analytically using the method previously proposed by the authors for solving a boundary value problem based on the parameter identification of a discrete model with the use of modal control. The simulation results demonstrating the effectiveness of the proposed algorithm, as well as the high accuracy level of the steady-state control, are presented.