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The Schur-Cohn test plays an essential role in checking the stability of one-dimensional (1D) random processes such as autoregressive (AR) models, via the so-called reflection coefficients, partial correlations, or Schur-Szego coefficients. In the context of two-dimensional (2D) random field modeling, one of the authors recently proposed a 2D AR quarter-plane model representation using 2D reflection coefficients estimated by a fast recursive adaptive algorithm. Based on such 2D reflection coefficients, we can therefore derive two necessary stability conditions for a 2D AR quarter-plane model. One of these conditions can be considered as an extension of the Schur-Cohn stability criterion based on the 2D reflection coefficients.