We give a randomized algorithm for testing satisfiability of Boolean formulas in conjunctive normal form with no restriction on clause length. Its running time is at most 2^{n(1-1/\alpha)} up to a polynomial factor, where \alpha = \ln(m/n) + O(\ln \ln m) and n, m are respectively the number of variables and the number of clauses in the input formula. This bound is asymptotically better than the previously best known 2^{n(1-1/\log(2m))} bound for SAT.