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I apply the algebraic classification of self-adjoint endomorphisms of ${\bfR}^{2,2}$ provided by their Jordan canonical form to the Ricci curvature tensorof four-dimensional neutral manifolds and relate this classification to analgebraic classification of the Ricci curvature spinor. These results parallelsimilar results well known in four-dimensional Lorentzian geometry. Theclassification is summarized in Table 2 at the end of the paper.

Algebraic Classification of the Ricci Curvature Tensor and Spinor for Neutral Signature in Four Dimensions