  The relation between the spectral decomposition of a self-adjoint operator
which is realizable as a higher order recurrence operator and matrix-valued
orthogonal polynomials is investigated. A general construction of such
operators from scalar-valued orthogonal polynomials is presented. Two examples
of matrix-valued orthogonal polynomials with explicit orthogonality relations
and three-term recurrence relation are presented, which both can be considered
as $2\times 2$-matrix-valued analogues of subfamilies of Askey-Wilson
polynomials.
