In this paper a bilinear dual-rate sampling self-tuning controller (STC) appropriate for estimating the parameters of a system at a `slow' rate and controlling the system at a `fast' rate is proposed. The numerical integration approach considered makes use of the trapezoidal rule or, as it is otherwise known, the Tustin approximation. Essentially the approach aims to convert the bilinear model from its continuous s-plane representation to its discrete z-plane representation; with use being made of two discrete time models corresponding to the fast and slow sampling rates. Simulation studies making use of a practical model of a high temperature heating plant application serve to illustrate the performance of the proposed dual-rate scheme. It is shown that the dual-rate approach offers potential advantages over an existing single-rate bilinear STC in terms of both improved tracking ability and disturbance rejection.