Recently Ismail, Masson and Suslov established a continuous orthogonality relation and some other properties of a -Bessel function on a q-quadratic grid. Askey suggested that the `Bessel-type orthogonality' found in the above paper at the -level really has a general character and can be extended up to the -level. Very well poised -fuctions are known as a nonterminating version of the classical Askey - Wilson polynomials. In this paper we prove Askey's conjecture and discuss some properties of the orthogonal -functions. Another type of the orthogonality relation for a very well poised -function was recently found by Askey, Rahman and Suslov.