  In the paper we prove an extension theorem for matrices with entries in
H^{\infty}(U) for U being a Riemann surface of a special type. One of the main
components of the proof is a Grauert type theorem for "holomorphic" vector
bundles defined over maximal ideal spaces of certain Banach algebras. The proof
is also based on the results of A.Brudnyi "Projections in the Space H^{\infty}
and the Corona Theorem for Coverings of Bordered Riemann Surfaces" (see my
previous submissions here).
