  We study a substitute for the matrix product ansatz for Asymmetric Simple
Exclusion Process with open boundary in the ``singular case''
$\alpha\beta=q^N\gamma\delta$, when the standard form of the matrix product
ansatz of Derrida, Evans, Hakim and Pasquier does not apply. In our approach,
the matrix product ansatz is replaced with a pair of linear functionals on an
abstract algebra. One of the functionals, $\varphi_1$, is defined on the entire
algebra, and determines stationary probabilities for large systems on $L\geq
N+1$ sites. The other functional, $\varphi_0$, is defined only on a
finite-dimensional linear subspace of the algebra, and determines stationary
probabilities for small systems on $L< N+1$ sites. Functional $\varphi_0$
vanishes on non-constant Askey-Wilson polynomials and in non-singular case
becomes an orthogonality functional for the Askey-Wilson polynomials.
