We generalize Bernoulli’s classical method for finding poles of rational functions using the rational orthogonal Malmquist–Takenaka system. We show that our approach overcomes the limitations of previous methods, especially their dependence on the existence of a so-called dominant pole, while significantly simplifying the required calculations. A description of the identifiable poles is provided, as well as an iterative algorithm that can be applied to find every pole of a rational function. We discuss automatic parameter choice for the proposed algorithm and demonstrate its effectiveness through numerical examples.