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The pseudo-ultraspherical polynomial of degree n can be defined(Ismail)by-C(λ)n(x)=(-i)nC(λ)n(ix)where C(λ)n(x)is the ultraspherical polynomial of degree n..The ultraspherical polynomials are orthogonal on(-1,1)for λ ＞-1/2 while the pseudo-ultraspherical polynomials are orthogonal on the whole real line when λ ＜-n.We discuss how an identity linking C(λ)n and-C(1/2-λ-n)n can be used to deduce properties of the zeros of the pseudo-ultraspherical polynomials from known properties of the zeros of the ultraspherical polynomials.