We propose a method for predicting RNA base pairing which imposes no restrictions on the order of base pairs, allows for pseudoknots and runs in O(mN2) time for N base pairs and m iterations. It employs a self-con-sistent mean field method in which all base pairs are possible, but with each iteration, the most energetically favored base pairs become more likely as long as they are consistent with their neighbors. Performance was compared against three other programs using three test sets. Sensitivity varied from 20% to 74% and specificity from 44% to 77% and generally, the method predicts too many base pairs leading to good sensitivity and worse specificity. The predicted structures have excellent energies suggesting that, algorithmically, the method performs well, but the clas-sic literature energy models may not be appropriate when pseudoknots are permitted. Website and source code for the simulations are available at http://cardigan.zbh.uni-hamburg.de/~rnascmf.