Despite the success of the relay-feedback system in autotune identification, it is well known that an ideal (on-off) relay-based identification can lead to significant error in the ultimate gain and ultimate frequency. Instead of taking remedial action after relay-feedback experiments, an approach is taken to re-design the experiment such that a better estimate of K-u and omega(u) can be achieved throughout the experiment. In this work, the saturation relay is employed instead of the conventional ideal relay. The analyses show that the saturation relay gives significant improvement in the identification of K-u and omega(u). However, too small a slope in the saturation-relay may also fail to generate sustained oscillation. A procedure is tested on linear and nonlinear systems for system identification and multivariable autotuning. Using the proposed method significant improvement can be achieved while maintaining the simplicity of the relay feedback test.