The dynamics of the driven dissipative two-state system is formulated in terms of an exact nonconvolutive master equation. The kernel is expressed as power series in the intersite coupling, in which the lowest order corresponds to the familiar noninteracting-blip approximation. We use this formalism to calculate the kernel systematically in all orders of the intersite coupling for weak damping, and we solve the affiliated master equation for high-frequency driving in analytic form. Our approach finds straightforward generalization to any multistate dissipative tight-binding system.