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In a previous paper (Semel & L opez Ariste 1999, hereafter referred to as Paper I) the authors found a new solution for the integration of the radiative transfer equation for polarized light (RTE). The present paper is a continuation of that work, and shows how this solution has been incorporated into a new numerical code for the integration of the RTE. This code, called DIAGONAL, is characterized by an analytical handling of most model atmospheres, diering in that from other codes. It gives exact solutions in new, non-trivial cases. In the general case when no complete analytical solution is available, the code resorts to a multi{layer technique, thus providing a solution that combines an approximated analytical model and a minimized residual treated linearly. The algorithm is shown both to be very stable and to reach a high pre- cision even for a small number of integration layers. This results in a very fast code. A comparison with DELO has been carried out. DIAGONAL is available, upon request to the authors.

DIAGONAL: A numerical solution of the Stokes transfer equation