In this paper we describe a method that can be used for Minimum Bayes Risk (MBR) decoding for speech recognition. Our algorithm can take as input either a single lattice, or multiple lattices for system combination. It has similar functionality to the widely used Consensus method, but has a clearer theoretical basis and appears to give better results both for MBR decoding and system combination. Many different approximations have been described to solve the MBR decoding problem, which is very difficult from an optimization point of view. Our proposed method solves the problem through a novel forward-backward recursion on the lattice, not requiring time markings. We prove that our algorithm iteratively improves a bound on the Bayes risk. © 2011 Elsevier Ltd. All rights reserved.