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1. Introduction. Let G be a connected Lie group and H a closed subgroup with Lie algebra ϊ) such that in the Lie algebra g of G there exists a subspace m with g = m + § (subspace direct sum) and [mϊflcnt. In this case the corresponding manifold M = G/H is called a reductive homogeneous space and (g,ϊj) (or {G,H)) a reductive pair. In this paper we shall show how to construct invariant pseudo-Riemannian connections on suitable reductive homogeneous spaces M which make M into an Einstein manifold. Thus from the formula for the connection at the point H^M we compute the Ricci tensor, Ric (X,Y) for X, Fem,Y) = rjC{X,Y) where C(X,Y) is the pseudo-Riemannian metric inducing the connection and η is a suitable real number.