  We study an ensemble of random matrices (the Rosenzweig-Porter model) which,
in contrast to the standard Gaussian ensemble, is not invariant under changes
of basis. We show that a rather complete understanding of its level
correlations can be obtained within the standard framework of diagrammatic
perturbation theory. The structure of the perturbation expansion allows for an
interpretation of the level structure on simple physical grounds, an aspect
that is missing in the exact analysis (T. Guhr, Phys. Rev. Lett. 76, 2258
(1996), T. Guhr and A. M\"uller-Groeling, cond-mat/9702113).
