An algorithm is presented for solving coupled-cluster (CC) equations by successive diagonalization of 2 x 2 matrices. It is more expensive than usual procedures, but it is capable of solving a CC problem where any arbitrary excitation is included in the cluster operator. Equation-of-motion coupled-cluster (EOMCC) excitation energies can also be determined by this method regardless of the type of excitations in the cluster operator and the space where the effective Hamiltonian is diagonalized. The algorithm is applied to the study of the convergence of CC and EOMCC series in some small bases.