Probabilistic model checking is a powerful method for analyzing quantitative properties of probabilistic systems. Its core is to calculate reachability probabilities. One prevalent method of computing these probabilities is value iteration, which performs one-way fixed point iteration to obtain an approximation to the true value but sometimes returns unreliable results. Three recently proposed sound methods — interval iteration, sound value iteration and optimistic value iteration — extended from value iteration ensure the accuracy of the returned results, and each method has its own merits and demerits. In this paper, we proposed a new sound method called bisection value iteration. Our method accelerates bounds convergence through bisection together with upper/lower bound verification and can be applied to model checking reachability and reward properties for Markov decision processes. It is easy to be implemented. The experiments show that our method performs well on a wide range of instances.