We derive the expression of an optimum non-Gaussian radar detector from the non-Gaussian spherically invariant random process (SIRP) clutter model and a bayesian estimator of the SIRP characteristic density. SIRP modelizes non-Gaussian process as a complex Gaussian process whose variance, the so-called texture, is itself a positive random variable (r.v.). After performing a bayesian estimation of the texture probability density function (PDF) from reference clutter cells we derive the so-called bayesian optimum radar detector (BORD) without any knowledge about the clutter statistics. We also derive the asymptotic expression of BORD (in law convergence), the so-called asymptotic BORD, as well as its theoretical performance (analytical threshold expression). BORD performance curves are shown for an unknown target signal embedded in correlated K-distributed and are compared with those of the optimum K-distributed detector. These results show that BORD reach optimal detector performances.