Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also includes a relatively small number of off-diagonal coefficients, selected according to the excitation amplitudes undergoing the largest change in the coupled-cluster iteration. A test case shows that the new inversion of partial matrix (IPM) method gives much better convergence than the straightforward Jacobi-type scheme or such well known convergence aids as the reduced linear equations or direct inversion in iterative subspace methods.