This paper presents a stochastic iteration algorithm solving the global illumination problem, where the random sampling is governed by classical importance sampling and also by the Metropolis method. Point pairs where radiance transfer takes place are obtained with random ray shooting. Ray shooting can mimic the source radiance and the geometric factor, but not the receiving capability of the target (i.e. the BRDF and the area), which results in not optimal importance sampling. This deficiency is attacked by the Metropolis method. The pseudo random numbers controlling ray shooting are generated not independently, but by the perturbation of the previously used pseudo random numbers. These perturbations are accepted or rejected according to the change of the contribution of the transfers. The algorithm is mesh based, requires only a few variables per patch, and can render moderately complex glossy scenes in a few seconds.