The authors introduce a missing family of orthogonal polynomials through limit of little \(q\)-Jacobi polynomials when \(q\) goes to \(-1\). The polynomials thus obtained are indeed classical and satisfy a three-term recurrence relation (which is a general feature of polynomials) and an eigenvalue equation with a differential operator of Dunkl type. Originally, the concept of orthogonal polynomials for \(q=-1\) was introduced by {R. A. Askey} and {M. E. H. Ismile} [Mem. Am. Math. Soc. 300, 108 p. (1984; Zbl 0548.33001)] for the \(q\)-ultraspherical polynomials. The authors also show that, these polynomials provide a nontrivial realization of the Askey-Wilson algebra for \(q=-1\) and they reduce to the ordinary Jacobi polynomials under certain specific conditions.