An alternate method is presented of obtaining the direct-interaction equations by combining the heuristic and rigorous derivations of Kraichnan. Within the framework of the model dynamic representation of Kraichnan's rigorous theory, we have developed the irreducible diagram expansion systematically * by formalizing the perturbation argument of his heuristic derivation. It is hoped that the present work will provide a further insight into the analytical structure of the irreducible diagram expansion and bridge the gap apparent in the two original derivations of the direct-interaction equations given by Kraichnan.