We present a modified GPU version of MrBayes, called ta(MC)3 (GPU MrBayes V3.1), for Bayesian phylogeneic inference on protein datasets. Our main contributions are (a) utilizing 64-bit variables, thereby enabling ta(MC)3 to process larger datasets than MrBayes, and (b) to use Kahan summation to improve accuracy, convergence rates, and consequently runtime. Versus the current fastest software, we achieve a speedup of up to around 2.5 (and up to around 90 vs. serial MrBayes), and more on multi-GPU hardware. GPU MrBayes V3.1 is available from http://sourceforge.net/projects/mrbayes-gpu/.