For a bilinear system that is open-loop neutrally stable, a quadratic state feedback control has been proposed to ensure global asymptotical stability of the closed-loop system. In this paper, a new nonlinear control is proposed so that the closed-loop system is not only asymptotically stable but also exponentially stable. The new control results in a much faster state convergence rate than the quadratic control; furthermore, it can be applied to systems with tight saturation limits on the control input.