In the standard linear, time-invariant feedback system, controllers that achieve diagonal decoupling and closed-loop stability exist if and only if the plant satisfies the diagonal denominator condition or has no coinciding poles and zeros in the region of instability. A simple and systematic decoupling design procedure is presented under each of these conditions. The closed-loop poles can be placed at any desired points, and free parameters are included for satisfying additional design objectives. The designs are also extended to provide integral action in order to track step inputs with zero steady-state error.