An algebraic design via Diophantine equations of dual-rate regulators for linear unstable and non-minimum-phase plants, generalizing the well-known constraints for the reference model in single-rate systems, is presented in this brief. This brief improves previous results achieving internal stability for this kind of plants, by means of adapting the Youla parametrization of all stabilizing controllers to the dual-rate case. A simulation example on a robotic model, as well as an experimental magnetic levitation setup, are presented.