The paper describes an improvement of the so-called TNO model to predict the noise emission from aerofoil sections due to the interaction of the boundary layer turbulence with the trailing edge. The surface pressure field close to the trailing edge acts as source of sound in the TNO model. It is computed by solving a Poisson equation which includes flow turbulence cross correlation terms. Previously published TNO type models used the assumption of Blake to simplify the Poisson equation. This paper shows that the simplification should not be used. We present a new model which fully models the turbulence cross correlation terms. The predictions of the new model are in better agreement with measurements of the surface pressure and far field sound spectra. The computational cost of the new model is only slightly higher than the one of the TNO model, because we derived an analytical solution for the turbulence cross correlation terms.