Solymosi and Raghavan (2001) characterize the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. Their proof makes use of some graphtheoretical tools, while the present proof relies on the notion of buyer-seller exact representative in Núñez and Rafels (2002)