We propose and study an iterative substructuring method for an h-p Nitsche-type discretization, following the original approach introduced in [Bramble, Pasciack, Schatz (Math Comp. 1986)] for conforming methods. We prove quasi-optimality with respect
to the mesh size and the polynomial degree for the proposed preconditioner. Numerical experiments asses the performance of the preconditioner and verify the theory.
