The tangential block decomposition for block-tridiagonal matrices is introduced, which is in many aspects similar to the ones being used in frequency filtering. In opposite to those methods, for the class of model problems this new approach does not use any test vectors for its implementation. Similar to many iterative methods, it needs only bounds for extremal eigenvalues. Theoretical properties of this scheme are similar to those for the ADI-method. Convergence analysis is given by test examples.