A distributed consensus algorithm in which every sensor maps its state value through a bounded function before transmission is proposed. It is shown that when the step size of the algorithm is chosen appropriately, the state values of all the nodes converge exponentially to the sample average of the initial observations provided that the transmission function has a bounded first derivative. The convergence factor is shown to depend on the derivative of the transmission function. The performance of various bounded transmission functions are studied through simulations. It is shown that by appropriately choosing the step size, the proposed algorithm could achieve the same speed of convergence as that of the best case linear consensus algorithm based on the Laplacian heuristic.