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In a few recent papers a new approach to the Kowalevski integration procedure has been suggested. That approach gave a possibility to generalize the Kowalevski integration procedure and to apply it to a whole new class of systems, so called the systems of the Kowalevski type. The method is based on a  class of polynomials – discriminantly separable polynomials, recently introduced by Dragović. Here, we investigate a relationship with an algorithm proposed by Franco Magri, so called Magri’s method of syzygies. The results are joint with Vladimir Dragović.