The stability of an equilibrium point of a Hamiltonian system with two degrees of freedom in the presence of combinational resonance is investigated. The combinational resonance supposes that the characteristic equation has two different double roots with the absolute values equal to unity, which are not equal to \(1\) or \(-1\). In Section 2 the problem is stated. The Hamiltonian is a \(2\pi\)-periodic function of time and analytic in a neighborhood of the equilibrium. The case of general position, when the monodromy matrix of the linear system has nonsimple elementary divisors is considered. The goal is to obtain the Hamiltonian normal form in the presence of combinational resonance, which furnishes the stability results of the considered system. In Section 3 the first stage of the normalization algorithm, namely the linear normalization is presented. The linear part of the symplectic map generated by the considered canonical system is normalized. In Section 4 the nonlinear normalization is presented. Finally, the Hamiltonian takes a form for which the stability was studied in detail in [\textit{A. P. Ivanov} and \textit{A. G. Sokol'skij}, J. Appl. Math. Mech. 44, 574--581 (1980; Zbl 0478.70025); translation from Prikl. Mat. Mekh. 44, 811--822 (1980)]. In Section 5 the proposed algorithm is used to perform the stability study of satellite oscillations.